Grover circuits at depth n report a bit with probability cos²((2n+1)θ). Each shot multiplies the likelihood over θ by that factor. The deepest rung draws a comb of identical peaks; every shallower rung is a vote that erases the wrong ones.
| r @ nmax | runs | wrong basin | catastrophic |
|---|
A run counts when all its shots are in. Wrong basin: estimate more than one basin from the truth. Catastrophic: more than ten.
The comb. With nmax = 64 the deepest rung's response repeats every w = π/(2·129) in θ. One shot there says "you are at one of these 65 places", all equally likely. That is a basin: the deepest rung fixes where you are within a tick, never which tick.
The votes. A shallower rung has a wider fringe, so its outcome favors some basins and disfavors others. Two or three shots per rung are enough, because "this tick or that one" is a yes/no question. Watch the amber fringe: where it is high the shot said "likely here".
Try r = 2. Powers of two space the rungs so far apart that each decision rests on one rung. Rival peaks tens of basins away survive far more often, and the estimate lands in the wrong basin. At r = 1.45 several rungs cover every scale and the comb collapses to one peak with single-digit shot counts.
What is fixed here. Depths are round(rj) up to nmax plus depth 0; the shot profile is one shot at the deepest rung and one more per shallower rung. Nothing adapts to the data. The truth is drawn fresh with "New draw".