We proposed an order parameter for grokking. Then we killed it.

A pre-registered falsification of H3, an original hypothesis proposing Fourier concentration of embeddings as an unsupervised order parameter anticipating the grokking transition. The signal works on modular addition but flips sign on modular multiplication (corr -0.562), and is beaten on all four runs by a trivial weight-norm baseline. A derived product (GenMon) collapses from 0.93 to 0.28 correlation off algebraic tasks. Verdict: KILL. Includes primary data, reproduction code, and a documented retraction of an invalid weight-decay experiment caught during pre-publication review.