A generator is paid to make a solver fail. It succeeds completely, and the problems it invents get measurably less difficult while it does. Every combination path is enumerated exactly in this page, so you can watch the objective come apart from the thing it was supposed to measure.
Three numbers, one target, four operators. There are exactly 108 ways to combine them. This page enumerates all of them in exact rational arithmetic and counts how many reach the target. That count is the ground truth the whole study is measured against — type anything you like and watch it compute.
Each tick on the left is one of the 108 combination paths, ordered by the value it produces. Lit ticks reach your target. Difficulty is −log₂ of the lit fraction, so a puzzle with one solution out of 108 scores 6.75 bits and one with twenty scores 2.43.
Both panes run real GRPO on the same puzzle space with the same reward. The left one is the original implementation: group-relative advantage, nothing else. The right adds the two fixes — an entropy bonus and an in-group duplicate penalty. Watch the left pane's gradient go to exactly zero and stay there.
What this instrument demonstrates is the zero-variance trap, and that part is arithmetic rather than fitted: when a sampled group is identical and the reward is saturated, the group-relative advantage is exactly zero and the policy cannot move, whatever the learning rate. Difficulty and solvability are exact. The solver's pass rate is a surrogate, because a 0.5B language model cannot run in a browser — calibrated against measured probe bins for the difficulty slope, the audited generator-versus-control gaps for the small-number effect, and the measured within-bin pass variance of 0.1397 for how much puzzles of equal difficulty differ. The separate finding about distribution shift is shown in section 03 from the real runs, not here.
Try it: on monotone hardness the original collapses onto a single puzzle the solver never solves, its reward pins at 1.0, and roughly half its updates die. Switch to edge-seeking and it still collapses to one proposal, but the reward stays noisy so the gradient survives — collapse and gradient death are two different failures.