Raw average price correction can give the wrong sign when comparing windows of the same Uniswap pool. Wang finds this in both main pools. In the 5 bp Ethereum pool (ETH5), mean same-block correction toward an external reference rises from 0.484 bp in Discovery to 0.580 in Confirmation. In the 5 bp Base pool (BASE5), it rises from 0.107 bp to 0.143. Give both windows the same distribution of discrepancy states and the Confirmation-minus-Discovery differences become -1.141 bp for ETH5 and -0.525 bp for BASE5. Both bootstrap intervals lie below zero.
The identity behind the comparison
A passive Uniswap v3 pool changes price only when someone swaps against it. Wang measures each block's absolute log gap between the pre-block pool price and an external reference, then records how much the gap closes by the end of the block. Without a focal-pool swap, correction is exactly zero. Within each bin, mean correction therefore equals the product of the block share (π), the probability of at least one swap (p), and mean correction conditional on a swap (m).
The discrepancy measure x divides the gap by -log(1 - fee). Thus x = 1 corresponds to about one fee width, roughly 5 bp here. Ten fixed bins divide the x axis; the final bin, [5, ∞), has no upper bound.
The external reference averages the log midpoints of Bybit ETHUSDC and OKX ETH-USDC best quotes. Each venue contributes its last quote strictly before the block timestamp. Both quotes must be no more than 3 seconds old; there is no single-venue fallback. Screening leaves 354,506 ETH5 blocks and 2,164,574 BASE5 blocks across 57 represented days between 9 June and 5 August 2026. Discovery covers 6 July to 5 August (30 days). The Confirmation holdout covers 9 June to 5 July (27 days), placing it earlier on the calendar.
The pre-specified test failed. Wang expected the slope in a swap-only hinge regression to increase beyond x = 1. Instead, the estimated changes were -3.653 bp per unit x for ETH5 and -1.478 for BASE5, with both intervals wholly negative. Restricting the sample to x ≤ 1.5 gives an ETH5 Confirmation estimate of +2.344. The tail is already implicated in the sign change.
Response-map transport followed that failure, and the author describes it as post-confirmatory. It takes the p and m maps from one window and applies them to the other window's state shares. A Shapley split attributes ETH5's raw change to composition at +1.256 bp, conditional magnitude at -1.171 and incidence at +0.011. Together they give the +0.096 bp raw change.
Does a swap close the gap?
The distinction between p and m matters at either end of the x axis. In ETH5 Confirmation's bottom bin, x below 0.25, swap blocks move price away from the reference by an average of -0.447 bp. The reference is fixed strictly before the block; the external market can move during it. At the other end, in [5, ∞), swaps occur in 12,871 of 12,885 blocks, yet their mean correction is only 0.468 bp.
As the paper puts it, "a block containing a swap does not by itself indicate that the discrepancy was corrected." Counting swaps as arbitrage would misread both cells.
One cell accounts for ETH5's 2.2 bp transport gap
Most of the headline size comes from one cell.
The [5, ∞) bin contains 0.06% of ETH5 Discovery blocks, against 7.6% in Confirmation. BASE5's corresponding shares rise from 0.01% to 5.3%. In ETH5 Discovery, the bin's estimated mean correction is 29.626 bp, based on 108 swap blocks. Using the paper's bin table, we applied that estimate to Confirmation's 7.6% share (0.0756 × 0.947 × 29.626). That cell supplies about 2.12 bp of the transported prediction of 2.792 bp. Realized mean correction is 0.580. To first order, this cell accounts for the -2.212 bp transport error.
Wang also reports capped results. With x ≤ 5, ETH5's standardized difference falls to -0.095 bp; composition contributes +0.217 and magnitude -0.085. The corresponding BASE5 figures are -0.106, +0.136 and -0.069. Every one of those intervals excludes zero. The reversal between raw and standardized comparisons survives this cap, too. At x ≤ 2, the pattern is not established.
Removing the tail preserves the direction while shrinking ETH5's size about twelvefold, from 1.141 to 0.095 bp. The caps renormalize bin weights, so subtracting the capped estimate from the full estimate would not isolate an additive tail contribution. The cell calculation above gives better evidence of how much the tail supplies. The abstract calls the magnitude "is support-dependent and amplified on full support," alongside its statement that the offsetting pattern survives tail removal. Both claims check out. The capped estimate deserves to be the quoted figure.
Decisions left to the implementer
The reference rule, fee normalization and ten bins are specified, along with bootstrap seeds (20260829 and 20260907), pool addresses and public code. Rebuilding the analysis still leaves three decisions.
Start with the tail. A state of x ≥ 5 means a gap of roughly 25 bp or more. ETH5's AMM-native hourly volatility ranks at the 37.6th percentile of its history when averaged across the full 57-day study window. As the paper notes, that calculation is not separate for Confirmation and cannot rule out a volatile June. In our view, reference misalignment warrants an audit before these observations are interpreted as market behaviour: 7.6% of Confirmation blocks are that far from the reference, swaps occur 99.9% of the time, and correction averages 0.468 bp. The paper leaves the mechanism behind the shift unidentified.
There is a related reference issue. About 6% of blocks pass the reference-validity flag yet have a non-finite reference value (377,250 flagged versus 354,506 analytic for ETH5). The author traces and removes these observations. Anyone reimplementing the analysis should log why they arise.
Then there are the clocks. Ethereum blocks arrive about every 12 seconds, versus about every 2 on Base. Per-block swap incidence therefore cannot be compared across chains. The paper explicitly declines to infer a chain effect from ETH5 versus BASE5; comparisons of cross-pool p levels require the same restraint.
Inference is the remaining decision. The sample has only 27 to 30 day clusters, and both pools share calendar dates. The author describes the intervals as descriptive and the cross-pool agreement as non-independent. The transport intervals also carry no adjustment for a design developed after the holdout failed.
Correction offers no tradable signal
C records a change in native price. The author explicitly distinguishes it from trading surplus, and gas, MEV and fill costs never enter the calculation. For orientation, the paper expresses ETH5's composition and magnitude contributions as about +25% and -23% of the 5 bp fee. Those percentages describe adjustment toward a reference. They say nothing about profit.
We could not run this ourselves. The analysis needs pool-level block states and swap events to identify blocks without swaps. It also needs synchronized Bybit and OKX best quotes no more than 3 seconds old. Minute ETH bars would destroy the exact identity on which the decomposition depends: no swap means zero correction.
Standardizing state shares is a practice worth adopting whenever AMM tracking is compared across windows. Our arithmetic under common weights attributes about 1.05 bp of the 1.141 to the ETH5 tail cell. Most of the full-support 1.141 bp reflects 108 swap blocks in the July-August Discovery window applied to an unexplained surge of 25 bp gaps in June.