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Fuji: The Shape, Composition, and Spread of Demand Bursts on Robinhood Chain

Pranay Anchuri

arXiv:2610.35738v1econ.EMcs.SIq-fin.TR

TL;DR

Fee mechanisms have been studied, but demand and trading activity during elevated-demand periods have not been measured. Using Robinhood Chain blocks and Uniswap swaps, the paper characterizes burst shape and composition; bursts peak at 2.5 times usual demand, and cascades fit their arrivals relatively better than self-excitation.

  • Problem

    Existing studies examine gas fee mechanisms, but do not model demand and activity during elevated-demand periods, even though bursts can overlap and differ in their concentration across pools.

    Source: §1 · p. 2

  • Method

    The authors analyze Robinhood Chain block records and Uniswap swaps, compare burst intervals with matched controls, and fit cascade and self-excitation models to burst arrivals.

    Source: §1 · p. 3, §2.2 · p. 5

  • Results

    Bursts peak at 2.5 times usual demand, trade about as many pools as quiet periods but mostly different ones, and cascade fits are relatively better than self-excitation.

    Source: §1 · p. 3, §8 · p. 18

  • Takeaways & Limitations

    Trader entries cluster for about 24 seconds beyond what the existing traders predict, but the paper leaves imitation versus a shared signal unresolved.

    Source: §1 · p. 3, §6.2 · p. 15

    The analysis covers one chain’s first three months and Uniswap swaps; imitation among traders is not causally identified.

    Source: §8.1 · p. 18

Abstract

from arXiv · show

Demand on blockchain-based marketplaces arrives in bursts and at a high rate. On these platforms the data are completely visible, which makes it feasible to compare the bursty demand against the usual load. The congestion manifests as an increased demand for gas, the primary resource a blockchain sells. Existing studies consider how to price the gas. The demand itself, and what it is made of during bursts, has not been measured. We measure it on Robinhood Chain, a layer-2 blockchain that quickly became a venue for trading tokenized equities and memecoins. We collected the data from every block of its first three active months and more than 50 million Uniswap swaps that occurred during bursty periods. We find that a burst trades about as many pools as a quiet period, mostly different ones, and trades them harder, on top of elevated demand that accumulated for hours. With the bursts aligned on their peaks, the median peak is 2.5 times the usual load. Both the rise and the fall of the demand are described by the sum of two exponential functions with different timescales, a slow one of hours and a fast one of minutes. Against a matched quiet period, a burst has 1.05 times the pools, 1.40 times the trades, and 1.21 times the senders. We use two models to explain the arrival of bursts: externally triggered cascades and self-excitation. The former fits the data relatively better. Inside a burst, the entry of each trader into a pool is followed for about 24 seconds by more entries than the existing traders predict. Whether this is because of imitation or because of a shared signal is left open.

1 Introduction

The paper asks how gas demand concentrates in time and across assets during bursts, a gap left by fee-focused studies. It measures Robinhood Chain bursts and analyzes their shape, trading composition, and clustering.

Shape of demand bursts

  • The peak of demand is 2.5 times the usual level and 1.6 times the demand 20 minutes away.The median burst profile is described by two exponential components with different timescales.Source: §1 · p. 3

Composition of bursts

  • A burst trades about as many pools as a quiet period, but largely different ones, with more trades and more participants.The trades account for the highest gas usage, and gas spent on reverting transactions roughly doubles inside bursts.Source: §1 · p. 3

Shape of demand bursts

  • The slow timescale is about 60 times the fast one, or about 40 times after controlling for the daily cycle.The 24-hours-prior control accounts for at most 38% of the slow rise before the peak.Source: §1 · p. 3

Clustering between and within bursts

  • Cascades fit burst arrivals relatively better than self-excitation, although the latter cannot be discarded.Within bursts, trader entries cluster for about 24 seconds, with a stronger effect in pools with more swaps.Source: §1 · p. 3

Composition of bursts

  • The leading pool by value holds about a sixth of a burst’s value, while the leading pool by trades accounts for about a sixth of its trades.Source: §1 · p. 3

2 Data

The paper uses Robinhood Chain’s public block and swap records to characterize its data, define burst periods, and assemble trading observations for analysis.

2 Data

  • Robinhood Chain is a public rollup producing about ten blocks per second, and the study uses on-chain data from 27 June to 28 September 2026.This covers the chain’s first three months of continuous operation.Source: §2 · p. 3

2.1 Definitions

  • A minute is busy when gas exceeds both 1.5 times the rolling 24-hour median baseline and that baseline plus 5 Mgas s−1.The authors derive burst intervals, peak-aligned 12-hour windows, and burst windows from the gas series and busy minutes.Source: §2.1 · p. 4
  • Windows longer than twelve hours are excluded, and those excluded windows account for 48% of all minutes above the threshold.Consequently, window-level results describe bursts only.Source: §2.1 · p. 4

2.2 Trading Data

  • The study analyzes Uniswap swaps and excludes routing pools, which route trades between pools.Swap records include pool, block, and trader for peak-adjacent periods; trade counts use 200 burst windows, while priced-trade analysis uses amount fields from 656 burst intervals.Source: §2.2 · p. 5
  • Burst-interval controls are equal-length periods 24 hours earlier, with comparisons based on a random sample of 150 non-overlapping controls.Uniswap trades account for 37.6% of gas in burst intervals.Source: §2.2 · pp. 4–5

3 Shape of the Demand Burst

The median burst profile has a slow shoulder and a rapid neck around a peak about 2.5 times the usual gas level. Two exponential timescales describe the profile, and a slow rise remains after controlling for daily activity.

3 Shape of the Demand Burst

  • The median profile is nearly symmetric, with a slow rise and fall surrounding rapid ascent and descent near the peak.The rapid portions are the neck; the slower portions are the shoulder.Source: §3 · p. 6, Figure 4 · p. 7

3.1 Burst Model

  • The peak reaches 2.54 times the usual level, while a single-exponential fit has about 1.6 times the error of the two-exponential fit on both flanks.The fast timescales are 2.7 minutes on the rise and 4.2 minutes on the fall; the slow timescales are 218.5 and 199.2 minutes, respectively.Source: §3.1 · p. 7, Table 3 · p. 8

3.2 Controlling for Time of Day

  • After controlling for the daily cycle, at most 38% of the slow rise is attributable to that cycle, and the slow timescale remains about 67–68 minutes.The control profile rises 0.23 from six hours to five minutes before the peak, versus 0.61 for the burst profile; the control may itself include recurring bursts.Source: §3.2 · p. 8

3.3 Phases in the Burst

  • The fast exponential governs most demand change during rise and fall, while the slow exponential governs build-up and decay.Individual bursts have a median ascent and descent duration of 0.8 minutes; the comparison of trading in core and margin does not identify the shoulder’s origin.Source: §3.3 · p. 9

4 Composition of a Burst

Bursts trade about as many pools as quiet periods, but mostly different pools, and trading activity is more concentrated in time. Trading value can rank pools differently from swap counts.

4 Composition of a Burst

  • Trading accounts for 37.6% of gas during bursts, while reverting transactions account for 17.1%, versus 8.5% outside burst periods.Token transfers and minting account for 30% of burst gas, compared with 42.1% outside bursts.Source: §4 · pp. 9–10

4.1 What Is in a Burst

  • Tokenized equities and funds lead 34% of burst intervals, and no burst has more than 90% of trading related to stocks.Within 30 minutes of the weekday stock-market open, 54.8% of bursts are equity-led, versus 34% overall.Source: §4.1 · p. 10, Figure 5 · p. 11
  • A pool’s swaps are about half as spread out in time as all swaps in the window: the median pool-window ratio is 0.23 versus 0.47 overall.This comparison covers 68,370 pool-window pairs with at least 50 swaps.Source: §4.1 · p. 10

4.2 Traders and Trading Frequency

  • The number of pools rises 1.05 times and swaps rise by a factor of 1.40 during bursts; only 40% of burst pools also traded in the control.The largest pool by value accounts for 17.6% of value versus 6.3% of trades, while the pool with the most trades accounts for 7.1% of value.Source: §4.2 · p. 11, §4.3 · p. 12
  • Only 15% of senders recur from a control period to the following burst, compared with 17% between consecutive non-burst periods.The chain’s address population turns over by 80% regardless of bursts.Source: §4.2 · p. 12

5 Models for the Arrival of Demand Bursts

Bursts cluster more tightly than independent arrivals or the daily cycle alone predict. Of the two arrival models, cascades fit better than self-excitation, though the evidence does not rule out self-excitation or establish the direction of the ether-price association.

5 Models for the Arrival of Demand Bursts

  • More than half of consecutive bursts are less than 30 minutes apart, versus 15% expected under independent arrivals and 24% under the daily-cycle assumption.Bursts concentrate during United States daytime hours and cluster more than the daily cycle explains.Source: §5 · p. 12, Figure 6 · p. 13

5.1 Cascades or Self-Excitation

  • The cascade model groups independent bursts under a common external event, while the Hawkes self-excitation model lets each burst raise the rate of the next.Both models include a periodic weighting factor to isolate the daily cycle.Source: §5.1 · pp. 13–14
  • Cascade arrivals score 0.268 versus 0.312 for self-excitation and 0.408 for the daily-cycle baseline; lower scores are better, but self-excitation cannot be excluded.The fitted cascade model produces 8.3 bursts per day, against 8.0 observed between the first and last burst.Source: §5.1 · p. 14
  • Ether moves 1.33 times as much in the ten minutes before a burst as at the same hour on other days, but recent bursts may themselves move the price.For bursts more than two hours apart, the effect is not detectable (1.09, p = 0.86), so causal direction cannot be identified.Source: §5.1 · p. 14

6 Spread of a Burst

The section tests whether traders enter pools in clusters beyond what a common trigger and the active-trader count predict. Excess entry autocorrelation decays over about 24 seconds, while trader entry timing also shows stable patterns across samples.

6.1 Entry Models

  • The common-trigger null predicts new entrants from active traders; the alternative allows existing traders to draw in later entrants.Excess autocorrelation subtracts the mean autocorrelation of bootstrap samples under the null, measured over lags from one to forty seconds.Source: §6 · pp. 14–15, §6.1 · p. 15

6.2 Entries Cluster Beyond the Common Trigger

  • Across 5,144 pool-windows, mean excess entry autocorrelation is +0.050, largest at one second and decaying with τk = 23.7 seconds.The interquartile range of τk across pool-window samples is [23.1, 24.3]; the one-second lag is excluded from the fit shown in Figure 7.Source: §6.2 · p. 15, Figure 7 · p. 16
  • Excess rises from 0.006 to 0.115 across the smallest to largest swap-count quarters, but shows no monotonic pattern across trader-count quarters.The trader-count-quarter excesses are 0.039, 0.120, 0.026, and 0.014.Source: §6.2 · p. 16

6.3 Trader Timing

  • Trader earliness correlates at +0.311 across two halves of pool-windows, and pairwise directed ordering among the 600 most active traders correlates at +0.377.The corresponding shuffled-label correlations are +0.001 and +0.007; the authors caution that stable ordering does not establish that one trader observes another.Source: §6.3 · p. 16

7 Related Work

Prior work studies congestion pricing, burst patterns, diffusion, and automated market makers, while this paper centers on measuring the shape, breadth, and arrival of demand bursts. The related literature also motivates distinctions between burst profiles, temporal correlation, and trader imitation that the paper tests or leaves unresolved.

Demand and congestion pricing

  • Blockchain and other-platform studies examine congestion pricing, fees, resource use, and user responses, treating demand bursts as inputs to pricing; this paper models their shape, breadth, and arrival.The discussion cites Roughgarden, Chung and Shi, and related blockchain and platform studies.Source: §7 · p. 17

Bursts and their arrival

  • Prior burst research models burst shapes, endogenous build-up, heavy-tailed intervals, and periodic Poisson cascades; this paper tests daily-cycle effects without establishing that its slow rise is endogenous.The paper uses the cascade construction of Malmgren et al..Source: §7 · p. 17

Diffusion and attention

  • Information-cascade and online-diffusion studies use social information or network content, whereas on-chain data here supports tests of trader time dependence, not observed exposure or attention.The token-rotation measure does not explicitly observe attention or exposure to social feeds.Source: §7 · p. 17

Automated market makers

  • Automated-market-maker research links bot competition and speculative arbitrage to gas use; the elevated share of gas spent on reverting transactions during bursts is consistent with that analysis.The cited bot studies include Daian et al. and Wu and Öz [30].Source: §7 · p. 17

8 Discussion

The discussion relates burst shape and clustering to the gas capacity and pricing a chain must accommodate. The study’s evidence is bounded by one chain, its first three months, Uniswap swaps, and limitations in burst detection and causal identification.

8 Discussion

  • The median burst peak is 2.5 times usual gas demand, with a five-minute-per-side neck and a two-hour-per-side shoulder; burst periods consume 12.2% of gas during 6.1% of the time.The discussion suggests a pricing mechanism may need components responsive to both the neck and shoulder; the arrival evidence favors cascades but cannot rule out self-excitation.Source: §8 · p. 18

8.1 Limitations

  • The analysis covers one chain’s first three months and Uniswap swaps; the slow timescale varies with the detection baseline, and trader imitation is not causally identified.The null model counts only each trader’s first swap, while repeated swaps can produce clustering without imitation.Source: §8.1 · p. 18

A.1 Data and Definitions

  • The trader sample contains 732,619 distinct traders across 13.7 million swaps near 200 burst-window peaks; two end-of-data bursts were removed by the alignment-window restriction.Thresholds in the burst definitions were chosen by inspection.Source: §A.1 · p. 21

A.2 Shape and Descent

The median burst profile is shown across aligned windows, and its rising and falling flanks are characterized by fast and slow exponential timescales. The descent correlations require caution because peak height and pre-burst level also determine the half-height threshold.

A.2 Shape and Descent

  • Figure 8 displays the spread of 654 aligned burst windows around the median profile.The windows are aligned on their peak minutes.Source: §A.2 · p. 21
  • The slow timescale is 218 to 282 minutes on the rise and 185 to 294 minutes on the fall, while the fast timescale is 2.2 to 3.6 and 3.3 to 9.8 minutes, respectively.The slow term is unidentified in nearly 6% of resamples on the rise, and the fast term is less certain on the descent.Source: §A.2 · p. 21
  • Peak height and pre-burst level both set the half-height threshold, so their correlations with descent duration partly reflect how that duration is measured.The 654 bursts have three hours of gas data on either side of the peak and both ascent and descent phases.Source: Table 7 · p. 22, §A.2 · p. 22
  • The fitted model reaches 2.16 at the peak, compared with 2.54 in the data, and excludes the peak minute from its two-exponential fit.At five minutes from the peak, the fast term retains 16% of its peak value on the rise and 31% on the fall.Source: §A.2 · p. 22

A.3 Composition

The composition, arrival, and spread analyses characterize burst activity across pools, burst timing, and trader entry. They report distinct pool activity, a qualified comparison between arrival models, and excess short-term trader entries under specified sampling conditions.

A.3 Composition

  • The median Jaccard index of pool sets in burst-control pairs is 0.25, and intersecting pools account for 35% of burst swaps.For the priced sample, the largest pool’s median share is 14.4%, a lower bound on the leading token’s share; the largest pools by value and trades coincide in 36% of bursts.Source: §A.3 · p. 23

A.4 Arrival

  • The estimated arrival-model margin is 0.043 with a simulation standard error of 0.009, but sampling uncertainty is not estimated, so self-excitation is not excluded.The fitted self-excitation model has a branching ratio of 0.69 and a decay time of 101 minutes.Source: §A.4 · p. 23

A.5 Spread

  • Excess autocorrelation is positive in 80% of the 5,144 qualifying pool-windows and exceeds two standard deviations in 44.3%.The analysis requires at least 200 swaps, 50 distinct traders, and 300 one-second bins per pool-window.Source: §A.5 · p. 24
  • The estimated entry-following interval is about 24 seconds, with a 23.1-to-24.3-second interquartile range, but conditioning on swap flow can absorb imitation.Unaccounted variations faster than the 300-second smoothing can also leave positive autocorrelation unexplained by the null model.Source: §A.5 · p. 24

B The Shoulder Test

The shoulder test compares burst-core trading with activity in the remaining window margin, but its overlap result cannot distinguish a current burst’s shoulder from a previous burst. The estimate for isolated bursts is also uncertain because it uses only 24 bursts and one flank.

B The Shoulder Test

  • In the median window, 96% of core trading is in pools that also trade in the margin, versus 92.9% for a random block of equal length.Core-margin overlap exceeds random-block overlap in 87% of windows, by a median of 0.02, but the test is not powerful enough to identify whether the shoulder belongs to the current or previous burst.Source: B The Shoulder Test · p. 24
  • The 24 isolated bursts have a 102-minute slow timescale, compared with 222 minutes for the remaining bursts, but the isolated estimate is uncertain.The isolated estimate uses only the falling flank and omits the daily-cycle correction; removing isolated bursts changes the slow-timescale estimate from 199.2 to 222 minutes.Source: B The Shoulder Test · p. 24

C Trader Timing Checks

Trader timing is measured as entry position within a pool’s active span, adjusted for the average entry position in that pool-window and the trader’s swap count. The resulting earliness measures and pair orderings show consistency across several splits.

C Trader Timing Checks

  • Entry position is the fraction of a pool’s active span at which a trader first appears, and the adjustment uses pooled ordinary least squares.The model relates each trader’s entry position minus the pool-window average to the log of that trader’s swap count in the window.Source: C Trader Timing Checks · pp. 24–25
  • Earliness is defined as the negative fitted residual, so positive values indicate entry earlier than the pool-window mean.The split-half comparison covers 123,285 traders across 2,708,314 trader-pool-window triples.Source: C Trader Timing Checks · p. 25
  • The 600 most active traders yield pair-ordering correlations of +0.377 across random halves, +0.346 across disjoint windows, +0.147 across disjoint pools, and +0.278 across time halves.After shuffling labels, the correlation is +0.007.Source: C Trader Timing Checks · p. 25

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