A passive edge in 1301.T moves by 1.010 bps when the cancellation rule changes. Across 18 held-out July dates, passive-at-touch shortfall falls from 9.018 to 8.008 bps when cancellations move from the back of the queue to the front. Most L2 execution backtests leave that choice unpriced.
Which order left the queue?
L2 shows total quantity at each price, without revealing the order of individual orders inside it. Consider a 100-share cancellation at the best bid. The quantity could come from ahead of your child order or from behind it, and the displayed decrease looks the same. Only a removal from the front brings your order closer to execution. A simulator filling passive orders from price-level data therefore carries an allocation rule, whether stated or hidden.
One variable, fixed paths
Danait, Zamora and Boier describe the problem as conditional partial identification. The observed aggregate path narrows the possible order-level histories without choosing among them. They reconcile a synchronized L1 trade feed with ten-level L2 snapshots, using the result to attribute market removals. Every retained side-price transition is classified as an addition or a cancellation.
Their path-preserving compiler converts this aggregate path into an order-level message stream. Across runs, it fixes aggregate states, reconciled removals, the latent order partition, additions, timestamps and episode boundaries. Only residual cancellation placement changes. The front rule removes the oldest eligible quantity, the back rule removes the newest, and quantity-weighted-random samples an order with probability proportional to its remaining size.
The reconstructed background streams then run through JAX-LOB, a GPU-capable matching engine written in JAX. This external replay checks whether the messages can execute mechanically outside the compiler. The test covers 648 streams built from 54 background paths for 1301.T, alongside 456 streams from 38 paths for 7911.T. Every market-message quantity executed, totaling 232,800 and 4,119,600 shares.
The proprietary LSEG Tick History sample comes from the Tokyo Stock Exchange and spans 6 January to 25 July 2025. It contains two instruments. The quieter one, 1301.T, has a 5 yen tick, 843,135 continuous L2 rows and 24,607 regular trades. The active name, 7911.T, has a 1 yen tick, 9,062,080 rows and 319,046 trades.
January to May provides the partition inputs and parent scale. June determines the block, probe and policy settings, leaving Eighteen July dates held out. Each instrument supplies 1,080 non-overlapping five-minute episodes. Those episodes cover 97.27% and 96.80% of continuous-session elapsed time.
Three price-taking shadow policies operate on the episodes: aggressive TWAP at ten checkpoints, passive-at-touch, and a hybrid that crosses any schedule deficit at those checkpoints. Passive children appear as virtual queue markers. They do not divert executions or change the replayed book. Implementation shortfall is measured against the arrival mid, and any residual inventory crosses on a copy of the terminal book.
Passive orders carry the sensitivity
For 1301.T, aggressive TWAP records 10.010 bps. The corresponding figure for 7911.T is 2.400 bps. Both remain identical under all three cancellation rules. Within this zero-impact price-taking design, queue ambiguity affects passive execution, while the taker-only cost model has no FIFO sensitivity.
Passive-at-touch shortfall for 1301.T is 8.008 bps under front placement, 8.418 under random placement and 9.018 under back placement. Preterminal completion, meaning the share filled before the terminal cross, is 18.15 / 15.29 / 10.14 percent. Front minus back comes to -1.010 bps, with a date-resampling interval of [-1.253, -0.788].
For 7911.T, the same shortfall sequence is 0.765 / 0.926 / 1.149 bps. Completion reaches 97.20 / 95.52 / 89.81 percent. Front minus back is -0.384 bps [-0.493, -0.284]. The hybrid is less responsive and changes by almost the same amount in each name: -0.398 and -0.414 bps.
Completion sensitivity is close across the instruments, at 8.01 versus 7.39 points. Cost sensitivity differs by a factor of nearly three. Under every rule, most passive inventory in 7911.T fills before the terminal cross, so a comparable completion gap produces a smaller cost range.
The desk-level asymmetry goes further. For 1301.T, the lowest-cost policy changes in 0.83% to 4.49% of directed cross-rule comparisons, with a conditional added cost of 14.277 to 17.354 bps. For 7911.T, it changes in 3.63% to 14.26% of comparisons, while the added cost is only 2.366 to 3.723 bps. Frequency rises as severity falls. The authors identify both sets as pooled descriptive statistics over observations that share dates and background paths. They provide no resampling intervals for them.
The 1.010 bps range is incomplete
The paper states the limits of its range directly. Its compiler class covers a strict subset of the compatible history set. Front and back, the authors write, "are endpoint conventions for cancellation location, not estimates of the historical queue". They also say the reported sensitivity set is "not the complete set of outcomes allowed by the data." The implication runs in one direction: 1.010 bps understates the identified width.
The authors add that their reported estimates "are not suprema or envelope widths over the full compiler class." The design offers no measure of how much wider the full range could be.
We did not find any comparison with market-by-order ground truth. JAX-LOB replay checks message routing and matching in an external engine, establishing mechanical validity. It does not show whether the reconstructed queue matches the historical queue. The latent partition is sampled from reconciled aggregate addition increments, which the authors acknowledge may combine several historical submissions.
Across this sample, ambiguity affects individual episodes while leaving the date-average ranking intact. Passive-at-touch remains cheapest for both instruments under every rule. Hybrid follows, then aggressive.
And the sample is thin.
It contains Eighteen held-out dates, two RICs and 36 instrument-day observations, as the limitations section states. Under the stricter replay-block check, 1301.T produces -0.397 bps [-0.576, -0.229]. The 7911.T result is -0.325 bps, with an interval of [-0.649, 0.000] that reaches zero. The authors caution that the strict and boundary-fixed analyses retain different episode samples. Their comparison therefore does not isolate boundary handling. The random rule uses only three seeds.
Absolute levels are not tradable numbers in any case. These shadow policies assume zero latency, no fees or rebates, no endogenous impact, and a terminal cross performed on a copied book.
Run both endpoints before trusting the edge
Run the front and back versions, then report both. The conditional fill ordering is proved only for a single tagged marker during one unchanged best-price spell. It further requires the random rule's ahead-of-marker removals to fall between the two endpoints.
The ordering held for all 354,774 (1301.T) and 370,992 (7911.T) matched probe triplets. Those triplets represent 22.84% and 18.12% of reconciled trade volume. A passive edge smaller than the endpoint spread belongs to the queue assumption. Taker strategies can skip the exercise: 10.010 and 2.400 bps did not change by a digit.
We could not reproduce any of this. The mechanism requires synchronized price-level depth snapshots and a trade-print feed so that market removals can be attributed. Our equity data consists of US daily and one-minute OHLCV, with no quotes, no depth and no prints. The study also uses proprietary LSEG data for Tokyo listings, which we do not hold.