Papers

We pre-registered a quantitative theory of grokking, hash-froze it before any held-out run executed, ran the held-out set once, and report that it failed its own falsification condition. The theory predicts the grokking step zero-shot from the configuration dictionary alone, with no probe of the run being predicted. Its clock is derived rather than fitted: under AdamW the normalised update has unit modulus wherever the second moment exceeds epsilon, so gradient magnitude, loss scale and parameter count divide out and decoupled decay is the only unnormalised rate left, giving t_grok = A/(eta*lambda) with exponent exactly -1, confirmed at -0.98, -1.11, -0.73 and -0.96 across four training fractions. On 80 configurations it placed 0.550 of rows within a factor of two against a committed 0.61: falsified. The failure is structured, not diffuse. Inside the task families it was fitted on it is unbiased (mean error +0.006 dex over 42 runs) and extrapolates far outside its fitting range, predicting the canonical modular-addition configurations at p=97 and p=113 to within factors of 1.2 to 1.7 having never seen a modulus above 59 or a two-layer model. On eight unseen task families it is biased +1.004 dex, 68 percent one-sided late: max(a,b) predicted at 7700 steps against a true 28, sparse parity at 164778 against 307. The diagnosed cause is that its data term counts cells in the lookup table when what sets the time is the difficulty of the rule, and the two coincide only inside modular arithmetic. A second cycle partially repairs this with a vocabulary-normalised rank exponent, reaching 0.538 under leave-one-task-family-out and turning parity from 2.677 dex wrong into a median error of 0.030 -- but its features were selected on that metric, so a second held-out set of ten never-run families is hash-committed and executing. We release the harness, 396 runs and both registries.