Straight answer to your question first: the absolute-threshold variant (Focal) is per-token with no global budget, depth is emergent, and on real text ~86% hit the R=4 ceiling anyway. That arm can't be cleanly matched, you're right.
But the percentile variant (Nomade) already is a fixed budget by construction. q=0.3 freezes the 30% least-uncertain active tokens every iteration, which gives a deterministic depth cascade (≈30 / 21 / 15 / 34% to full depth) independent of the data. q is the passes-per-sequence knob you're asking for.
So the clean ablation falls straight out of that, exactly as you're framing it:
- Entropy arm: percentile q=0.3, freeze the lowest-entropy 30% each iteration.
- Random arm: freeze a random 30% each iteration.
Same q → identical depth distribution → identical pass budget. The only thing that differs is which tokens spend it. Any remaining gap is the selection signal, cleanly isolated, no confound from freeze count.
And it's a tiny change: swap the entropy-quantile mask for a random mask at the same fraction, same seed, same harness. That's article 4's core experiment now, matched-budget, selection is the only free variable.
Thanks you turned a vague "entropy vs random" into a properly controlled one. (Pending the hardware fix, but the design is locked.)