At a hypothetical 5 bp per leg, Gate.io's apparent ETH triangles almost vanish: 120 five-second states survive, 64 forward and 56 reverse. The largest static profit bound is 3.36 USDT. Wen's study is therefore most useful to a trader as an account of which historical quotes can be trusted. Wen identifies the audited long-horizon reconstruction as his incremental contribution and treats historical-data authority as part of the estimand. Yet the paper does not test how much the sample depends on its handling of negative-amount rows, whose meaning the archive does not define.

How the quotes become a triangle

Ether trades against USDT on Gate.io directly and through BTC. Multiplying ETH/BTC by BTC/USDT gives a synthetic ETH/USDT price. Because the trades share a venue and matching engine, a difference between the direct and synthetic prices matters when it exceeds the spreads you must cross. A forward triangle buys BTC, buys ETH with it, then sells ETH for USDT; the reverse runs the other way.

Wen reconstructed best bids and offers for all three books from Gate's public hourly order-book archives, covering January 2022 through June 2023. He sampled an exact five-second grid of 9,434,880 timestamps. At each timestamp, a leg qualifies only after a full snapshot has initialised its book. Replay must have no malformed row or sequence break, the book must be uncrossed, and its latest update must fall within the same hour and no later than the timestamp. A failure quarantines that market until the next full reset. Of 39,312 expected market-hour files, 39,147 exist. All three legs qualify together at just 4,391,146 timestamps (46.54%); none qualify before 2022-09-16. The Terra crash in May 2022 consequently has no jointly ready three-leg rows.

On those valid rows, the median signed wedge is +0.164 bp and the median absolute wedge 1.416 bp; p99 absolute is 6.555 bp. Wen also reports an "exact and fresh" subset: all three legs have the same recorded archive timestamp, and each quote is at most one second old. Its 1,573,304 rows have a median absolute wedge of 1.433 bp.

Why do so many gross signs turn positive?

Cross the displayed bids and asks before fees, and 20.25% of forward rows and 18.61% of reverse rows show a positive gross edge. Within exact and fresh, the shares fall to 14.48% and 13.63%. Those counts sound large beside the spreads on the liquid legs: median ETH/USDT spread is 0.062 bp, and BTC/USDT is 0.043 bp. ETH/BTC, though, has a median spread of 4.164 bp. A small move in that wider book can change the gross sign while leaving little to collect.

Wen's exact log decomposition puts 90.66% of forward friction and 90.67% of reverse friction on ETH/BTC. Median gross edges are negative (-2.405 bp forward, -2.686 bp reverse), with p99 edges of 3.906 and 3.763 bp. Roughly one row in five crosses zero by a sliver. Even the 99th percentile falls short of a single 5 bp charge on one leg.

Fees, size and duration

With an equal 5 bp charge on each leg, 64 forward and 56 reverse rows remain from 4,391,146. At 10 bp the counts are 6 and 3; at 15 bp, Gate's published VIP0 taker rate in July 2022, they are 2 and 1.

Wen limits each triangle to the smallest displayed best-level quantity across its three books. Across all ready rows, median forward capacity is 49.64 USDT. For the 5 bp survivors, the median static profit bound is 0.0001 USDT forward and 0.0009 USDT reverse. The 64 forward rows make up 42 episodes. Median duration is one grid row; the longest runs 25 seconds. In the principal domain of the Q2 2024 comparison, both venues' quotes are no older than 5 s across 77,580 rows. It yields one 5 bp survivor, a Gate reverse row lasting one five-second key, with a 0.031271 USDT static profit bound.

The paper describes these quotes as "identify fee-sensitive static arbitrage bounds, not completed three-leg trades or realized trader-specific returns," and presents the study as an extension of Muck et al.'s live Binance result across a longer horizon. I agree with that reading.

The harder question comes before fees.

Quarantine determines the sample

All those figures depend on readiness. The archive has 54,975 malformed rows, including 52,470 SET rows with negative amounts that Gate's schema never defines. Wen declines to assign them a meaning, a defensible choice. MALFORMED_ROW quarantine, triggered by those rows and the other malformed rows, then extends across 9,749,313 of 28,304,640 single-market grid rows. The liquid books take much of the readiness loss: ETH/USDT is ready 48.65% of the time and BTC/USDT 49.39%, compared with 86.45% for the thinner ETH/BTC cross.

The excluded hours differ, too. On common support, hours with zero valid triangles have mean absolute ETH/USDT returns of 50.30 bp versus 34.23 bp, realized volatility of 57.13 versus 44.78 bp, and median spreads of 0.4227 versus 0.2171 bp. Price states exist for only 56 of those 160 hours. Wen makes no missing-at-random claim, applies no correction, and says so. I accept conservative replay as a data rule: it never silently repairs a book. Its consequence is that the 1.416 bp anchor and 120 survivors come from hours with lower observed volatility (SMD -0.3610, measured on the 56 zero-ready hours with prices). Quarantine dropped the excluded hours; the negative-SET rule is one part of that decision. Treating negative SETs as deletions or signed updates, recovering those hours, and finding unchanged wedge tails would change my view. I did not find that sensitivity in the body.

Exact-and-fresh episodes give another warning against reading gross incidence as tradable profit. USDC/SVB has a higher gross-positive forward share than FTX, 23.28% against 5.08%. Yet at 5 bp, FTX leaves 13 forward survivors and SVB none forward (four reverse). The episodes switch order after fees.

The paper's Data Availability line says no datasets were generated or analysed. That sits awkwardly beside a nine-million-row reconstruction and the code archive in Online Resource 2.

Minute bars cannot check this result

We did not backtest it. Our BTC and ETH data stops at minute OHLCV; it has no bid/ask, per-update source timestamps or displayed best-level quantities. Those are needed beyond the midquote. A minute close also smears the 4 bp ETH/BTC spread driving this result.

For a desk, Wen's filter is the durable finding. Gate.io's 99.58% file coverage yields 46.54% usable three-leg time, while triangles clearing the 15 bp VIP0 fee occupy three rows across 288 eligible days (September 2022 to June 2023).