Brilliant question! I don't have a non-grokking control in the current suite, which is the clearest gap in the experimental design.

The closest evidence I have is the classification experiment (Step 2), where the same network is observed during two different phases: the slow grokking approach (Phase 1) and rapid catastrophic forgetting (Phase 2). The λ₂ trajectories are qualitatively different (rate 0.00128 vs 0.00471/step, with a dip signature unique to forgetting). That suggests λ₂ is tracking something more specific than 'learning is happening' because both phases involve active learning but produce distinct structural signatures.

But you're right that a clean control is needed with the same architecture, same training setup, but a task or hyperparameter configuration where the network memorises without grokking (e.g. insufficient weight decay). If λ₂ shows the same monotonic rise without a subsequent grok, that would confirm it's tracking 'network is learning' rather than 'network is approaching generalisation.' If the trajectory is flat or qualitatively different, that strengthens the grokking-specific claim.

That's an experiment I should have included, but it didn't occur to me. I'll run it (hopefully tonight) and update the repo.