Would any other famous number work just as well? No.
Built from square-root-of-2, pi, or e instead of phi, the same grid machine performs just as well, so the pre-registered test for "phi is special" fails.
Aggregates exclude the shared, constant-free 500 midpoint from each ratio set; the follow-through half of the pre-registered test is withdrawn as uninterpretable (it was tracking level spacing, not which constant drew the grid), so only the hold-rate half stands as the verdict.
Hold rate (aggregate
Follow-through rate
Out of every 100. The line marks 50.
The grid this system draws is built out of the golden ratio, phi. This study asked a colder, narrower question than "does the grid work": if you build the exact same grid machine – same swing anchors, same bookkeeping, same placement formula – but swap in a different famous number (the square root of 2, pi, or e) instead of phi, does the market treat those lines any differently than it treats phi's lines?
We wrote the pass/fail rule before running the study, and we are reporting exactly what it says.
The rule needed two things to both be true: phi's hold rate has to beat every alternative's with no overlap, and phi's follow-through rate has to do the same.
First half: FAIL. Phi's hold rate (71.9%) is not clearly higher than the alternatives'. Square root of 2 actually comes in higher (74.8%), and phi's own range overlaps it. Pi (71.7%) and e (71.2%) are statistically indistinguishable from phi. Phi does not separate from any of the three fakes on this measure.
Second half: withdrawn, not a pass. Phi's follow-through number (36.2%) did come out highest, with no overlap against any of the three alternatives – on its face, a clean pass. But when we checked the one level every set shares (the shared midpoint, which carries no constant at all), that level's own follow-through score ranks the four sets in the exact same order as the full result: phi highest, then e, then pi, then square root of 2. A level with no constant attached to it cannot be carrying a "phi property" – what it's actually tracking is how far apart each set's other levels happen to be spaced, and phi's set happens to be the most tightly packed of the four. So this measurement was quietly reading level spacing the whole time, not which number drew the grid. We are withdrawing it as a pass rather than keep a result we can't defend.
Combined verdict: FAIL. The first half failed outright, and the second half can't be credited because it wasn't measuring what it was built to measure. Stated as plainly as we can: on this test, the market does not treat a phi-shaped grid any differently than it treats a grid shaped by numbers that were never supposed to be special. That is a real result, not a shortfall in the study – it says something true about what the earlier flat hold-rate readings across rungs (see the linked entry) were actually showing us.