The Search-Space Atlas

Machine-readable summary

Every figure below is generated at build time from the same artifacts the interactive plates draw from, so no script has to run to read this page. The interactive version above is the same numbers with controls on them.

Study: is the grammar wide enough?

Every boundary that was a CUT rather than a structural floor was extended and re-measured, with each new level compared against the old boundary at identical coordinates on every other axis. A 5-minute opening range, a zero buffer, a 5-minute entry window and a zero volume filter are floors, not cuts, and cannot be extended.

Study: the relative-volume axis, run past the grammar's ceiling

Verdict: STILL IMPROVING. the median Sharpe is +0.051 at 20x and +0.245 at 50x against the 15x boundary, against a typical step on this axis of 0.079, and 83% of the 10,260 paired configurations move the same way. The upper boundary is still unresolved. The boundary tested was 15.0000x; the furthest level with enough sample to evaluate was 50.0000x; levels 80x, 120x are sample-starved and their figures are reported but not relied on.

No simulation was re-run for this: the threshold is applied by selection over outcomes the simulation already produced, so grammar v3's Plane C (0f8e339a980b) and ratio cache (e0e2c650eb92) were read unchanged.

Study: does any of the structure persist?

The pooled atlas is taken apart by calendar year and by the market's overnight gap. Findings, stated as the artifact states them:

• The overnight gap is the strongest conditioning variable in the project, and it does not survive being taken apart by year.
• Persistence is not regional: the configurations that were positive in 13 of 18 years fall into disconnected pieces, and not one has an interior cell — every member has a neighbour that failed.
• No stop at all beats both OR-width and ATR stops on every persistence measure, on one common eligible sample.
• Universe size is a plateau, not a peak.
• The grid is not four stocks: the median configuration traded over a thousand distinct names.

Grammar v3, 143,640 configurations, 4,531 sessions, 2005-01-03 to 2022-12-30.

Study: the stock's own gap — direction, or magnitude?

The first per-position state variable in the project: each stock's own overnight gap in its own ATR units, over 7,728,361 (stock, session) cells, so two names held on the same morning land in different bins. The finding is that the effect is SIGNED, not a breakout. An up-gapping stock beats a flat-opening one by +0.1516 Sharpe with 68% of 143,507 paired configurations agreeing, and a down-gapping one loses -0.2797. But a big move in EITHER direction against a quiet open — the contrast an opening-range breakout actually predicts — is worth -0.0818 at 43% agreement, which is a coin.

the frozen ORB definition triggers only on the UPSIDE — the first bar closing above the opening range high plus a buffer — and has no short side. So an up-gap helping and a down-gap hurting is consistent with the day's directional drift reaching a long position, and this study cannot separate that from a breakout effect. The magnitude contrast can: a breakout edge should show up when the open is unusual in EITHER direction. The unconditioned median across all 143,640 configurations is -0.4904: every difference below is a difference between two losing portfolios, and the level is printed beside it for that reason.

Study: universe depth — what did the top 500 buy?

UNRESOLVED AT THE UNIVERSE BOUNDARY. the universe artifact stops at 500 names, so a quantity still moving at the last rung is a statement about where the data ends, not about where the effect does. Nothing here extrapolates past it. Plane C stores each session's tickers in universe rank order, so a top-N portfolio is a prefix sum along the ticker axis and all 500 values of N come out of one cumulative sum rather than 500 reductions.

No N is recommended. The best-performing N exists in any sample and is the same kind of artifact as the best cell of the parameter grid. What is reported instead is where four quantities stop changing, and they can settle at different depths. Shape and ranking are measured on all 143,640 configurations; level, spread and drawdown on a 2,054-configuration sample (54 points of the lattice's own skeleton plus a seeded draw, chosen by geometry and by seed, never by result).

What this is not

Not a recommendation to trade an opening-range breakout. The grid loses money gross of costs across almost all of its configurations, and the subject of the project is the shape of the search space rather than the strategy in it. No level or configuration on this page is recommended, and the boundary studies deliberately classify axes by whether an effect has STOPPED, never by whether a level performed well.