The 50bp slippage cap degrades the sqrt model to flat-fee across the whole admissible-but-thin cohort

[eaitbrahim]

Raised in docs/presentations/se.md §9.3 and backed by a measured shadow run. Distinct from #335: that issue is about the promotion gate still pricing at the flat 5bp fallback. This one is about the cap binding even where per-product pricing is already used.

The finding

slippage_for_quote_volume is floor × sqrt(anchor / median_daily_quote_volume) clamped to [5bp, 50bp]. The cap binds at 100× below the anchor — $5M/day median — while the admission floor is $1M/day.

Every asset in that 5× band is simultaneously admissible and capped, and that band is essentially the entire realistic candidate universe. Across the cohort the square-root model degenerates into a flat-fee model — which is the modelling defect #259/#334 shipped to remove. It was removed for the liquid half of the universe and silently retained for the thin half.

Measured, using keel's own slippage_for_quote_volume:

asset	median daily	model demands	actually used
CRO	$1,139,342	104.7bp	50.0bp	capped
PAXG	$1,224,999	101.0bp	50.0bp	capped — and LIVE
STX	$1,300,933	98.0bp	50.0bp	capped
OP	$2,585,800	69.5bp	50.0bp	capped
ATOM	$3,084,518	63.7bp	50.0bp	capped
FIL	$3,294,287	61.6bp	50.0bp	capped
JASMY	$4,161,283	54.8bp	50.0bp	capped
BTC (control)	$568,943,908	4.7bp	5.0bp	—

It is already in the live book. PAXG is allowlisted and capped at 2.0× understatement. The rest of the live set is inside the live sqrt region (BTC 5.0, ETH 6.2, DOGE 20.5, ADA 23.9, XLM 35.4bp).

Measured magnitude — a shadow run at a 150bp cap

At a 150bp cap the clamp is inert for this cohort (max demand 104.7bp), so the run measures what the shipped model already computes and is currently overridden on. turtle_breakout, hourly, full cached history:

asset	n	net @50bp	net @150bp	rel decline	cost ×
CRO	248	0.3195	0.2428	24.0%	2.09×
STX	243	0.2932	0.2276	22.4%	1.96×
OP	221	0.2894	0.2605	10.0%	1.39×
ATOM	268	0.2172	0.2007	7.6%	1.27×
FIL	261	0.4167	0.3904	6.3%	1.23×
JASMY	271	0.6774	0.6663	1.6%	1.10×
PAXG	74	0.0465	0.0155	66.7%	2.02×
BTC / ETH (controls)	293/282	0.1471 / 0.2388	unchanged	0.0%	1.00×

Controls frozen to the digit; gross PF invariant across cells; nothing net-positive in either cell. PAXG is excluded on sample size (n=74, below the floor) — its 66.7% is arithmetic on a net PF of 0.0465.

Relative decline is perfectly monotone in the cost multiple across every asset above the sample floor — 2.09/1.96/1.39/1.27/1.23/1.10 maps to 24.0/22.4/10.0/7.6/6.3/1.6%.

The honest reading — this is not urgent, and that is the argument for doing it

The cap is masking severity, not viability. Nothing was net-positive even at 50bp; the whole cohort sits between 0.1471 and 0.6774. Uncapping shifts that to 0.1471–0.6663. The bias is real and worth 1.6%–24% of net PF, and it changes no verdict, because every verdict was already negative. The binding constraint remains the 1.2% taker fee.

So the case for fixing it is not performance. It is that the bias is inert only while everything is far below break-even, and it activates precisely when something approaches 1.0 — which is exactly when nobody will be hunting for a silent quarter-turn of flattery. Fixing it while it costs nothing is the cheap moment.

Options, none of them obviously right

1. Raise or remove the cap. 150bp is a research value chosen to make the clamp inert; as a shipped constant it would be arbitrary. Principled versions: remove it, or set it from the corpus tail (~184bp for TON, which is what the current cap's own docstring reasons about).
2. Add participation-rate scaling. The model scales by the asset's liquidity and not at all by the size of the clip — a $50 order and a $50,000 order in CRO are both charged 50bp. This would also retire the cap's own justification, since "the 1-unit notional this engine fills" would stop being an implicit assumption and become an explicit input.
3. Raise the admission floor to $5M/day. Closes it from the other end — every admitted asset would land in the live sqrt region by construction. But it disqualifies every current shortlist candidate and live PAXG at $1.22M, so it is a policy decision, not a modelling one.

The current configuration does none of the three.

Acceptance criteria

• The cohort no longer receives an identical, capped rate regardless of its actual liquidity, or the cap is documented as a deliberate floor-on-pessimism with its cost stated.
• Whatever ships, keel simulate's per-product table keeps printing floor/cap/anchor beside every result so a number's assumptions stay recoverable.
• A control asset above the cap threshold (BTC/ETH) is unaffected — regression-tested.
• If the admission floor moves instead, live PAXG's status is decided explicitly rather than by side effect.

Notes

• PAXG's own median is measured on 470 daily bars (PAXG-USD since 2025-05-08). Cross-checked against the cached PAXG-USDT series (1,826 bars, 2021-07 → 2026-07): median $3,386,380 → 60.8bp, so the short window understates its longer profile by 2.76×. It is capped in both views, so the finding holds; only the magnitude moves (2.02× → 1.22×).
• Related: Opt the promotion gate into per-product slippage — prerequisite-gated on a thin-asset candidate or a load-bearing restatement #335 (promotion gate still on flat 5bp — the other half), slippage is one global 5bp constant applied from BTC to TON #259/feat(backtest): per-product slippage scaled from liquidity — assumed, capped, and reported (#259) #334 (the per-product model), and the thin-asset backtest-flattery caveat those carry.