The reversal of stale order-flow signals
and the latency-information frontier
The order book, the flow signal, staleness, and the three scores
A stock does not have one price. It has a queue of buyers and a queue of sellers, each stating a price and a number of shares.
The quote is the best bid and the best ask: the prices at which someone will sell to you or buy from you right now. The price is the midpoint between them. The gap is the spread, measured in ticks of one cent.
The touch is the shares waiting at the two best prices. Orders at a price fill in the order they arrived, so the 90 shares at 100.00 are ahead of anything posted there later.
Every message changes the book: an order added, cancelled or executed. A full NASDAQ session holds 280 to 370 million messages for our 58 stocks, about 13 every millisecond and far more in bursts.
In the high-priced stocks the touch has thinned since 2019.
| 2019 | 2025 | |
|---|---|---|
| Best quote holding fewer than 100 shares | 46% of the session | 85 to 88% |
| Median touch | 581 shares | 172 shares |
| Median spread | 1.6 ticks | 3.4 ticks |
| Unit | How long | Something that takes about this long | In this paper |
|---|---|---|---|
| 1 nanosecond (ns) | a billionth of a second | light travels about 30 cm | the simplest trading rule, wired into a chip, answers: 1.0 ns |
| 1 microsecond (µs) | a millionth of a second | a thousand nanoseconds | a tree-based statistical model answers on one processor core: 2.4 µs |
| 1 millisecond (ms) | a thousandth of a second | a deep-learning model of the book answers: 1.7 ms | the horizon we score. After a burst of buying, the first price change now arrives within 1 ms in 39 to 45% of events |
| 10 ms | a hundredth of a second | ten million nanoseconds | the delay at the centre of the paper: the signal acted on 10 ms late |
| 100 ms | a tenth of a second | roughly a blink of the eye | the window the trading signal looks back over; a mid-sized language model answers in 252 ms |
| 1 second and more | about a heartbeat; a frontier language model answers: 0.75 to 2.8 s | the 1 s and 60 s horizons, where every model is close to a coin |
Each tick on the axis is ten times the one before; the rule on the chip and the language model are nine orders of magnitude apart. Across the 58 stocks the book receives roughly 13 messages every millisecond on average, and far more in bursts.
Order flow over the last 100 ms is buying pressure at the best prices minus selling pressure. New bids and buys that hit the ask count as buying; new asks and sales into the bid count as selling.
| An illustrative 100 ms window | Buying pressure | Selling pressure |
|---|---|---|
| Orders placed at the best prices | 500 shares of new bids at 100.00 | 400 shares of new asks at 100.02 |
| Trades | 300 shares bought from the ask at 100.02 | 200 shares sold into the bid at 100.00 |
| Cancellations at the best prices | 100 shares of asks cancelled | 150 shares of bids cancelled |
The rule, which we call the flow rule: if buying dominated over the last 100 ms, predict that the mid moves up over the next millisecond; if selling dominated, down. Here: net buying, so the signal says up.
Acted on instantly it works: right 68 to 76% of the time in every half-year from 2019 to 2026 (in the high-priced stocks, 69.0% in 2019 H1 and 68.0% in 2026 H1). A coin scores 50%.
A second signal, the depth imbalance: which side of the book has more shares waiting. It scores 46 to 55%, and it does not reverse at any delay.
The signal says up. Acting on it means sending a buy order into this book, and there are two ways to do that.
Take: buy the 120 shares offered at 100.02 now. Certain, but you pay half the spread: one cent on USD 100, about one basis point (a basis point is one hundredth of one percent).
Make: post your own bid at 100.00 or a cent better and wait for a seller. You earn the spread if a seller comes, but you may not be filled, or be filled just as the price turns down.
Event 3: the price fell without a trade. The buyers’ own best bid was cancelled and the midpoint dropped. This event comes back in the mechanism section.
A seller hits the bid. The same new mid as event 3, by a different message: an execution against the bid.
What we score is the move in the mid after your order arrives: the information value of the decision before any cost. The mid only moves when a best price changes, and these are the four ways it does.
| Four events that move the mid | New best | New mid | For a buyer who acted on "up" |
|---|---|---|---|
| 1 A buyer takes all 120 shares at 100.02 | ask 100.03 | 100.015 | with the buying: up |
| 2 A buyer posts a bid at 100.01, inside the spread | bid 100.01 | 100.015 | with the buying: up |
| 3 The 90 shares bid at 100.00 are cancelled | bid 99.99 | 100.005 | against: own side pulled |
| 4 A seller sells 90 shares into the bid at 100.00 | bid 99.99 | 100.005 | against: down |
The book you saw
The book your order meets, 10 ms later
The book your order meets differs from the book you saw. The shares you meant to buy may be gone, or the bid beneath them cancelled. The age of the information when the order arrives is its staleness, written L in the draft. Every decision has one.
The paper measures which of the two happens when the signal is acted on late, and when it changed.
| Acted on | Right in 2019 H1 | Right in 2026 H1 | Reading |
|---|---|---|---|
| instantly | 69.0% | 68.0% | the signal works |
| 1 ms late | 56.1% | 56.3% | weaker, and unchanged across the years |
| 10 ms late | 55.2% | 38.0% | weaker in 2019, wrong in 2026 |
No model is credited for a move that happened while it was computing: the move is scored from the moment its order would have arrived.
The share of price moves whose direction the signal called correctly. A coin scores 50%.
The same share, weighted by the size of each move. Right on the small moves and wrong on the large ones scores below 50% here while above it by count.
The average signed mid change per decision, in basis points (hundredths of one percent), before any trading cost. The quantity a trader cares about.
19 sessions, 2019 to 2026; every order rebuilt from 280 to 370 million messages a day. Answers which technology wins at each speed, and what moves inside the book. Independent test days: 2 in 2019, 3 in 2026.
60 new days, two per quarter from 2019 Q1 to 2026 Q2, chosen by a calendar rule written down before the data were pulled; simple rules only, no fitted models. Answers when the reversal happened, in sign and in money. 60 independent days.
The best quote across eight exchanges on four days in 2019 H1 and four in 2026 H1; the official national best bid and offer on 1 and 2 July 2026. Answers whether it is one exchange’s screen or the national price.
A flow signal acted on 10 ms late in the high-priced stocks: right 55% of the time in 2019, right 38% of the time in 2026
Each point is a half-year of the high-priced stocks: four confirmatory days. H1 and H2 are the first and second halves of the calendar year. The whiskers are 95% intervals.
1 ms late: above 50% throughout; 55 to 56% in the last two half-years. The turn has not reached one millisecond.
100 ms late: 55 to 63% in 2019 and 2020; below 50% from late 2021; 41% in 2026 H1.
10 ms late: at or above 50% through early 2024, then 48, 49, 44 and 38%.
38% right means 62% wrong on these moves. From 2025 H2 the whiskers sit entirely below 50%.
The delay at which the signal stops being right moved from beyond 100 ms to about 10 ms, in stages. The pre-registered single clean flip was rejected; the dating is reported as found.
| 2019 H1 | 2024 H2 | 2025 H2 | 2026 H1 | |
|---|---|---|---|---|
| How often right | 55% | 48% | 44% | 38% |
| How much of the movement right | 53% | 41% | 41% | 38% |
| The money, bps per decision | +0.001 | −0.005 | −0.006 | −0.015 |
The money score, which the draft calls the markout: the average signed mid change per decision for someone following the 10 ms-old signal, in basis points. A basis point is a hundredth of one percent, one cent on USD 100.
Positive in 2019 and 2020. Negative with the interval clear of zero from 2024 H2, a full year before the count fell below 50%.
In 2024 H2 accuracy was 48%, close to chance, and the wrong calls fell on the larger moves: the movement-weighted accuracy was 41% and the markout was negative.
The markouts are small per decision; the spread paid to trade is many times larger. What matters is the sign: a trader watching the markout would have flipped the signal a half-year before one watching accuracy.
| Among the 23 high-priced names | Names with a significant downward break | Median break date | Middle half of the dates |
|---|---|---|---|
| 10 ms late, how often right | 18 | August 2024 | May 2022 to February 2025 |
| 10 ms late, the money | 16 | April 2025 | July 2024 to December 2025 |
| 100 ms late, how often right | 10 | January 2022 | May 2021 to July 2024 |
US stocks trade on more than a dozen venues. The same signal, on the same moments on 1 and 2 July 2026, scored against three prices:
The exchange’s displayed best bid and ask: the book we have been looking at.
−0.0124 bps per decision
The National Best Bid and Offer: the best bid and best ask across all US exchanges, counting round lots of 100 shares only. What a broker must honour and a retail investor sees.
−0.0124 bps: exactly as much as NASDAQ’s quote
Includes odd lots, orders of fewer than 100 shares, which can sit inside the official spread without changing the NBBO. In the high-priced stocks most quotes at the touch are odd lots.
−0.0063 bps: about half as much
2019: the sellers give way
2026: the buyers’ own bid is pulled
| First price move within 10 ms of a burst of buying | 2019-20 | 2025-26 |
|---|---|---|
| Goes with the flow: sellers give way, or a buyer improves the bid | 64% | 56 to 60% |
| Goes against it because the buyers’ own best bid is pulled | 15% | 18 to 23% |
| The same, at ordinary moments with no burst | 14% | 18 to 25% |
| Goes against it because a seller hits the bid | 4% | 7 to 8% |
| Share of bursts whose first price move arrives within 1 ms | 30% | 39 to 45% |
The same shift at ordinary moments with no burst at all: a general change in how liquidity is provided in these stocks, quotes placed and pulled within milliseconds.
Whether a pulled quote was fleeting, or a duplicate cancelled after a fill on another exchange, is not visible on one exchange’s book.
This is event 3 from the order-book slide, happening far more often. The whole of the fall in the with-flow share is the flow’s own side withdrawing; sweeps and refills on the other side did not rise, and the first move arrives sooner.
| The worry | The check | What survives |
|---|---|---|
| The signal counts a new bid as buying, so a pulled bid reverses it mechanically | Split the signal into executed trades only and quotes only; score each 10 ms late on the same moments | Trades alone reverse at least as strongly: right 38.6% with −0.023 bps, against 39.8% and −0.021 for the full signal |
| The tiny quotes at the touch are the whole story | Rebuild the best price from the first level holding at least 100 shares; compare the two books on common support (the same moments) | Same on either book: right 55% in 2019-20 and 46% in 2026; the 100-share best is displaced against the flow within 10 ms in 24% of events, against 17% |
| It is NASDAQ’s own flow | Recompute buying pressure across the eight exchanges and across the seven others; score on the official NBBO | Right 38.9% with NASDAQ flow, 38.7% with national flow, 40.1% with other-exchange flow |
| It is the spread opening and closing | Moments with a one-tick spread at both ends; the price defined as the microprice, a mid weighted by the shares on each side | One-tick moments are under 1% of moves and stay above 50%; on the microprice the signal is right 42% in the last two half-years |
These checks protect the measurement of the reversal. None of them identifies its cause.
Every trading technology timed on its own hardware, from a one-nanosecond rule to language models, and scored at the moment its order would arrive
A model with more capacity reads more from the same snapshot of the book; a slower model acts on an older snapshot. The frontier measures which effect is larger at each prediction horizon.
| Technology | What it does with the book | Time to answer |
|---|---|---|
| A rule in a chip (an FPGA: a chip whose wiring is programmed for one computation) | compares a handful of numbers | 1 nanosecond |
| A tree ensemble on one processor core | 300 trees over 25 features | 2.4 microseconds |
| A deep network on a GPU | a convolutional model of the book | 1.7 milliseconds |
| A frontier language model over the API | reads the same numbers as text and answers; the open models are read at their internal score for up against down, which is faster than text | 0.75 to 2.8 seconds |
The reversal adds to the cost of delay: if the response to flow has come and gone before a slow model has finished computing, the slow model is late and also wrong.
The sweep marks the time since the book was read. In the high-priced stocks the first price move after a burst arrives within a millisecond in 39 to 45% of cases, before the deep network has answered and before any language model has.
For each time budget, the best accuracy among the technologies that fit inside it, each scored at that delay. "No delay" is what the best model would score if it could act instantly; it is the reference for the cost of delay.
The next millisecond: 79% with no delay, 79% at 10 µs (the tree ensemble), 62% at 1 ms, 54% at 10 ms. Most of the loss sits between 100 µs and 10 ms.
Ten milliseconds ahead: the same shape, lower.
At longer horizons the curves flatten: at 60 s every technology is within a point of a simple rule.
Speed was worth half a point up to 10 µs and 17 points by 1 ms; cleverness at most 8 points, and only where speed was also available.
In money, the most confident decile of decisions earns 1.01 bps at 10 µs and 0.11 at 1 ms, against a half-spread of 2.4 bps, so no latency budget pays a trader who crosses the spread.
At horizons of a second or more, a second of delay might matter less and capacity more. The test:
With no delay charged, the language models read the book well: the two largest beat the simple rule for horizons of 10 ms to 1 s (65 to 68% against 62 to 66%) and edge the tree ensemble at 1 s and 60 s on a small sample.
Charged for the seconds they take, all four are close to chance (49 to 54% at 1 s ahead). A reasoning budget lifts one of them from 65.6 to 69.3% with no delay and adds nothing at its own latency (51.0%).
Accuracy predicting 1 ms ahead, by latency budget. The 2019 models scored unchanged on later days, then refitted on December 2025 and scored on 2026.
| Test days and model vintage | no delay | 10 µs | 100 µs | 1 ms | 10 ms | Edge kept at 1 ms |
|---|---|---|---|---|---|---|
| 2019-20 test days, 2019 models (116) | 79.2% | 78.7% | 75.8% | 62.2% | 53.5% | 42% |
| 2021, 2019 models (55) | 77.9% | 77.6% | 75.1% | 58.1% | 52.1% | 29% |
| December 2025, 2019 models (249) | 74.3% | 73.7% | 70.2% | 56.9% | 53.5% | 28% |
| 2026, 2019 models (146) | 70.7% | 70.0% | 66.1% | 56.3% | 51.9% | 30% |
| 2026, models refitted on December 2025 (146) | 73.2% | 72.3% | 68.1% | 57.3% | 59.5% | 31% |
Up to 10 µs nothing changes: 96 to 99% of the no-delay edge is retained in every era. The whole shift sits between 100 µs and 10 ms, where the queue now reacts. A signal one millisecond old kept 42% of its edge in 2019 and under a third in every later era.
Retraining recovers the no-delay point; the stale cells stay low: about half of the no-delay loss is model drift, nearly the whole of the stale loss is the market. The last row’s 10 ms cell is a model trained for its own delay; the flow rule at that cell scores 41.4%.
| Policy at the stale cell | Right [95% interval] | Money, bps per decision | After paying the spread, bps |
|---|---|---|---|
| Follow the flow signal | 41.4% [39.7, 43.2] | −0.0087 | −8.8 |
| Do the opposite | 58.6% [56.8, 60.3] | +0.0087 | −8.8 |
| Do the opposite of a model trained for no delay | 56.6% [55.0, 58.1] | +0.0032 | −9.0 |
| A model trained for its own 10 ms delay | 59.4% [57.8, 60.9] | +0.0103 | −13.1 |
| Trained model minus "do the opposite" | +0.8 points [+0.1, +1.5] | +0.0016 [−0.0014, +0.0043] |
Learning pays where the signal is fresh relative to the horizon: at 1 ms late predicting 10 ms ahead, the model beats the flipped rule by 3.4 points and 0.088 bps per decision.
After paying the spread, no policy makes money as a taker at any cell. What the stale cell offers is its sign, and a half-year of markouts reveals the sign in time.
A framework for technology choice, the literature, the next steps, and how the work could grow
A trading technology is a pair, how clever and how slow, and its value per decision is the money it earns at the moment its order arrives. Three things follow from the measured frontier.
| Literature | What it established | What this paper adds |
|---|---|---|
| Price response to tradesBouchaud et al. 2004; Lillo et al. 2003; Taranto et al. 2018; Campigli et al. 2022 | A trade’s price impact is partly temporary; models of how it decays, in trade time; time-varying impact at the scale of trades and days. | How that response at the millisecond scale changed over years, dated on pre-registered days, and what it does to a signal that arrives late. |
| Speed and absorptionBudish et al. 2015; Menkveld and Zoican 2017; Chordia et al. 2005, 2018; Hasbrouck and Saar 2009; van Kervel 2015 | Speed as a race for stale quotes; order flow absorbed within seconds to hours; fleeting orders and the liquidity mirage as two readings of quote withdrawals. | Absorption measured at the millisecond scale, at the queue, across years, and a frontier that prices latency against capacity for a prediction. |
| Learning in marketsAït-Sahalia et al. 2022; Hedges 2026; Liu 2026; Dugast and Foucault 2018 | The value of a millisecond of data for one model class; compute against latency on a benchmark data set; single hardware rungs; raw fast data against processed slow data. | Measured latencies from 1 ns to seconds on real books, every prediction scored at arrival, the stale cell as the reversal and the flipped rule as the benchmark any model must beat. |
The contribution sits at the junction of the three: a dated change at a fixed arrival delay, joined to value and to technology choice.
This is how I see the work growing: three parts, on the same data and the same scoring rule.
The dated reversal and the frontier: the useful life of order-flow information, scored at arrival, by market, year and technology. Every new chip or model class is a new rung on the same ladder; every tick-size, lot-size or batch-auction change re-dates the turn.
With multi-venue or participant-level order data: how liquidity is supplied and withdrawn within milliseconds, and which reading of the own-side withdrawal survives. A model of quote provision at that scale, tested where the reversal lives.
The value of a decision at the moment its order arrives as the primitive; speed and capacity as the choice; batch intervals and speed bumps as the levers, with implications testable on the same books.
What keeps it relevant: policy is moving on the objects this measures (the round lot for high-priced stocks changed on 3 November 2025, the half-penny tick is now due in November 2027, batch auctions and speed bumps are live design levers), the frontier can be re-estimated for every new technology, and scoring at arrival is a method later work can adopt.
The reversal of stale order-flow signals
and the latency-information frontier
| Layer | Training and construction | Held-out evaluation |
|---|---|---|
| 2019 frontier | 30 Jan, 27 Mar, 30 Jul and 30 Aug 2019; validation 30 Oct 2019; 30 May and 18 Oct 2019 enter the nine leave-one-day-out folds | 30 Dec 2019 and 30 Jan 2020: 116 stock-days, 2.9 million states |
| Out of time | 2019 models scored unchanged | 13 Jul 2021 (55 stock-days); 8 to 12 Dec 2025 (249); the 2026 days (146) |
| 2026 era models | 8 to 11 Dec 2025 training; 12 Dec 2025 validation; the 28 Nov 2025 half session is descriptive only | 15 May, 18 May and 12 Jun 2026: 146 stock-days |
| Confirmatory dating | Calendar rule fixed before the pull; 58 names carried forward by symbol; rules only | 60 new dates, two per quarter, 2019 Q1 to 2026 Q2; none among the days above |
| National price | Eight direct feeds rebuilt at the union of update times; official NBBO from Daily TAQ | 2019 H1 and 2026 H1 confirmatory days (eight venues); 1 and 2 July 2026 (official NBBO) |
Large tick. At or below 0.5 already in 2019 at 10 ms; at 100 ms as low as 0.24 by 2026 H1.
Mid tick. Near 0.5 at 10 ms (0.48 to 0.56 in 2019-20), 0.47 in 2026 H1; below 0.5 at 100 ms throughout.
Small tick. Above 0.5 through early 2024, then 0.48, 0.49, 0.44 and 0.38. The whole late transition is here.
By value the groups crossed: the large-tick 10 ms markout went from negative in 2019 to zero or slightly positive; the small-tick one from positive to negative.
The 1 ms control has one earlier point estimate just under one half, 2023 H2 at 0.479, and sits at 0.55 and 0.56 in the last two half-years: the preliminary draft’s "never reverses" wording will be narrowed.
An ex ante sign rule: the sign of the 10 ms-stale rule fixed for each half-year from the previous half-year’s markout within the group chose "reverse" in 9 of the 10 half-years from 2021 H1 and beats always following, by markout, in 8 of 15 half-years; it loses in 2023 H1 and, by count, in 2021 H1, the two half-years whose preceding markout was negative by less than 0.001 bps.
2026 H1 paired gain: +0.0296 bps per state, symbol-day interval [+0.0219, +0.0387], day-level [+0.0271, +0.0337]. Chosen by the previous half-year’s sign accuracy instead, the rule reverses from 2025 H1 and wins in four half-years: value turned before sign.
| Sample | NASDAQ mid | Eight-venue all-size best | Official NBBO |
|---|---|---|---|
| 2019 H1, four sessions, 65 stock-days | 0.552 [0.533, 0.566]+0.0009 | 0.568 [0.552, 0.582]+0.0016 | not available |
| 2026 H1, four sessions, 99 stock-days | 0.379 [0.361, 0.399]−0.0148 | 0.412 [0.394, 0.430]−0.0063 | not available |
| 1 and 2 July 2026, 56 stock-days | 0.392 [0.369, 0.415]−0.0124 | 0.412 [0.391, 0.434]−0.0063 | 0.389 [0.370, 0.409]−0.0124 |
| July 2026, the 17 names whose round lot is 100 shares (34 stock-days) | 0.371 [0.343, 0.399]−0.0157 | 0.385 [0.357, 0.411]−0.0086 | 0.364 [0.340, 0.387]−0.0166 |
| Signal component | 2019-20 | 2025 (December days) | 2026 |
|---|---|---|---|
| Full flow signal | 0.542 [0.533, 0.552]+0.001 | 0.420 [0.399, 0.443]−0.013 | 0.398 [0.381, 0.418]−0.021 |
| Executed flow only | 0.541 [0.530, 0.551]+0.001 | 0.408 [0.384, 0.430]−0.015 | 0.386 [0.365, 0.407]−0.023 |
| Quoted flow only | 0.530 [0.521, 0.538]+0.001 | 0.439 [0.421, 0.457]−0.010 | 0.411 [0.396, 0.426]−0.018 |
Executed flow alone, acted on 10 ms late, loses as much as the full signal; the quote construction cannot by itself explain the reversal. The two parts agree in sign on about three quarters of these states.
← Backup menu| h \ L | no delay | 100 ns | 1 µs | 10 µs | 100 µs | 1 ms | 10 ms | 100 ms | 1 s | 10 s |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 ms | 0.792 | 0.731 | 0.731 | 0.787 | 0.758 | 0.622 | 0.535 | 0.552 | 0.533 | 0.514 |
| 10 ms | 0.737 | 0.667 | 0.667 | 0.732 | 0.700 | 0.604 | 0.568 | 0.540 | 0.520 | 0.517 |
| 100 ms | 0.705 | 0.652 | 0.652 | 0.702 | 0.672 | 0.617 | 0.608 | 0.561 | 0.528 | 0.507 |
| 1 s | 0.656 | 0.621 | 0.621 | 0.653 | 0.634 | 0.599 | 0.582 | 0.585 | 0.544 | 0.509 |
| 10 s | 0.590 | 0.573 | 0.573 | 0.589 | 0.580 | 0.564 | 0.558 | 0.556 | 0.538 | 0.511 |
| 60 s | 0.542 | 0.537 | 0.537 | 0.537 | 0.534 | 0.529 | 0.527 | 0.525 | 0.520 | 0.514 |
A validation-selected policy (the model chosen per cell on 30 October 2019, scored once on the test days) is within 0.5 points of this envelope at 55 of 60 cells; the largest gap is 1.7 points, in near-chance cells. Nine leave-one-day-out folds over the 2019-20 days: oracle 0.787 to 0.819, the 1 ms cell 0.627 to 0.649.
← Backup menu| Technology | Latency | Platform | Boundary measured |
|---|---|---|---|
| Flow and imbalance rules | 1.0 ns | FPGA VU47P, Vivado 2025.2 | register to register, 3 logic levels |
| Rules in C | 5.9 ns per call | one pinned Xeon 8488C core | computation on a core, features in registers |
| Logic-gate network, 4 × 1024 gates | 8.2 ns | FPGA VU47P | register to register, 15 levels, 4,483 LUTs |
| Logistic regression, 25 features | 9.1 ns (57.5 ns in C) | FPGA VU47P, fixed point | register to register, 28 levels, 2,662 LUTs |
| LightGBM, 300 trees × 63 leaves | 2.37 µs median | C generated by tl2cgen, one core | per-call CPU time, batch one |
| DeepLOB, six horizon heads | 1.70 ms median | NVIDIA L40S | GPU inference, batch one, host to host |
| Qwen 4B and 27B logit read-outs | 109 ms and 252 ms | NVIDIA L40S, vLLM for the 27B | prompt in, logit out, batch one |
| Claude Haiku, Sonnet, Opus and Fable | 0.75 to 2.81 s median | API from the same region | round trip, numbers-only prompt of about 540 tokens |
| Question | What the evidence supports |
|---|---|
| Does reversing the rule make money? | A positive midpoint value remains negative after the half-spread: −8.8 to −13.1 bps per traded state for every taker policy in 2026. No net strategy is demonstrated. |
| Does learning ever help? | Yes, where the signal is fresh relative to the horizon: at 1 ms of staleness and h = 10 ms the tree adds 3.4 points and 0.088 bps per state over the reversed rule. |
| Who loses from the reversal? | Decisions that follow 10 ms-old flow without other information. Late prints (5 to 15 ms after an event) move the taker’s way, close to ordinary-moment takers; no participant class is identified. |
| What causes the change? | Own-side withdrawals are observed and have become more common at ordinary states too. Fleeting quotes against cross-venue quote management is not separable on one exchange’s book. |
| Is this a result about AI? | Only on a shared numerical information set and the tested library: at sub-second horizons latency outweighs capacity, and a reasoning budget adds nothing net. Text-reading models would be a different rung. |
| → space click | next click, then next slide |
| ← backspace | one click back (a slide back lands on its final state) |
| shift + → / ← | whole slides |
| number + enter | go to a slide |
| P | presenter window: audience view, the state after the next click, notes, timer |
| N | notes panel in this window |
| O | overview of every slide |
| A / Q | technical backup menu / back to the closing slide |
| F | full screen |
| B or . | black screen |
| R | replay this slide’s animation |
| T | reset the timer |
| Home / End | cover / closing slide |
The dots at the bottom right count the clicks left on the slide; when they are all filled, the next click moves on.