F-0019 · first recorded 2026-08-22
Holding trade size against the standing book fixed, a book thinner than three-quarters of its own daily normal costs about 20% more — so the ratio absorbs most but not all of the stress regime
PRELIMINARY
| Observation | across 985,950 aggressive bursts, median cost at a burst/depth ratio of 0.01-0.02 is 1.88 bps when the book is below 0.75x its day's median, against 1.62, 1.54 and 1.62 bps in the three deeper regimes. The pattern repeats at every ratio band: 0.98 vs 0.80-0.83 at 0.005+, 3.24 vs 2.58-2.74 at 0.02+. Only the thinnest band separates; the other three are indistinguishable |
|---|---|
| Sample | 985,950 same-side aggressive bursts of $50,000 or more, 22 days sampled every 60 days across Binance futures BTCUSDT from 2023-01-01 to 2026-06-14, joined to bookDepth within ±1% |
| Method | contiguous same-side aggTrades within 200 ms grouped into one burst; cost is executed VWAP against the price at which the burst began, signed against the taker; depth regime is the standing ±1% notional divided by the same day's median, so the split is "thin for this market" rather than "thin for 2023" |
| What is not established | the daily-median regime is not the same stress F-0002 measured, which was depth AFTER a large move relative to before — a sharper and rarer condition this test does not isolate. Bursts within a day are not independent. The high-ratio cells above 0.05 remain empty, so nothing is established about large trades |
| Who else publishes this | every execution model assumes a static book; none states whether its own estimate survives the regime where it would be used |
| Evidence | market/impact2.py run_stress, market/CONTRACT-impact.md K4, research/QUEUE.md Q6 |
market/CONTRACT-impact.md lists five kill conditions. K4 is the one that would have mattered
most:
the relationship reverses or vanishes in the stressed-depth regime — i.e. it holds only when it is useless
This is the first kill condition this project has tested and not fired.
The measurement
Cost paid in bps, by how thin the book is against its own daily normal, and by trade size against that book. If the ratio were sufficient, the rows would be flat.
| book vs day median | 0+ | 0.005+ | 0.01+ | 0.02+ |
|---|---|---|---|---|
| < 0.75× | 0.10 | 0.98 | 1.88 | 3.24 |
| 0.75–0.9× | 0.02 | 0.82 | 1.62 | 2.68 |
| 0.9–1.1× | 0.00 | 0.80 | 1.54 | 2.74 |
| > 1.1× | 0.01 | 0.83 | 1.62 | 2.58 |
They are nearly flat, and the exception is consistent.
The ratio does almost all the work. Moving across a row multiplies the cost three- to fourfold. Moving down a column changes it by a fifth at most. One number — size against the book standing in front of you — carries the relationship.
But the thinnest regime is genuinely more expensive, by roughly 20%, at every ratio band tested, in the same direction each time. The three deeper regimes are indistinguishable from each other, so this is not a gradient: it is a threshold that only bites once the book has lost a quarter of its usual depth.
What it means for the model
The book does not merely shrink under stress — its shape changes slightly too, and a cost estimate calibrated on ordinary conditions understates by about a fifth exactly when someone would want it. That is a small correction, and it is the kind that only exists because it was looked for.
It is also the second time F-0002’s finding has been confirmed from a different direction: depth withdrawal during large moves is real, and here it shows up as a residual the size-ratio cannot absorb.
What this does not establish
This is not the stress F-0002 measured. That was depth after a large move divided by depth before it, falling to 0.657 in the worst quarter — a sharper and much rarer condition. “Below 0.75× the day’s median” includes quiet overnight thinness, which is not the same event. The real stress premium may be larger than 20% and this design cannot see it.
And the tail is still empty. Every cell above a ratio of 0.05 has too few observations to
report, which is CONTRACT-impact.md P2 unresolved. Nothing here says anything about a trade
large enough to matter to a large account.