Structure-Specific Representational Priors Causally Control the Grokking Delay

Grokking -- generalization long after training-set interpolation -- has been accelerated by structure-agnostic interventions (gradient filtering, weight-norm clamping, geometric penalties). Whether the delay specifically measures the time to form task-structured representations has remained observational. We test it causally by injecting representational priors of varying content into a one-layer transformer learning modular addition, via a supervised-contrastive loss whose positives encode (i) the task's true structure ((a+b) \bmod p), (ii) a coherent-but-wrong sibling ((a-b) \bmod p), or (iii) a random partition -- all with identical loss form, strength, class sizes, and geometry. Whether generalization occurs follows a clean gradation: true 22/30 runs, sibling (same periodic features, wrong combination) 14/15, random (only memorizable) 0/20 (Fisher p=1.3\times10^{-7}). A weight-norm-matched control replaying the norm trajectory onto plain cross-entropy generalizes 0/15, ruling out the norm as mediator. Probes show structure formation precedes and predicts generalization in all runs. Only the true structure also accelerates grokking (up to 2.75\times), but this is dose-dependent and bimodal. We then confirm the mechanism by prediction: because the acceleration is gated by a weight-norm side-effect, clamping the norm during training yields a reliable, standalone accelerator with a median 8.6\times speedup (up to 22\times on the fastest seeds, under 1000 epochs), growing monotonically as the norm is held lower; the residual stalls also vanish, though significant only pooled over the two mitigations run at both strengths (0/40 vs 6/20, p=7.7\times10^{-4}), not per method. The grokking delay is, causally, the time to form the right representational structure -- decided at the level of features, not labels.