If you pay strangers to train a model, you cannot check the weights without redoing the work. Refereed schemes re-execute one disputed step and accept it if it lands within a tolerance, because honest workers differ by floating-point drift. We measured what that tolerance hides.
On a 64-64-10 MLP trained on the scikit-learn digits data (20 seeds), a worker that skips any step whose update is small enough to pass the check gets away with 30% of the steps at a tolerance of 1e-2, and the held-out loss moves by less than one seed standard deviation. The loss only suffers at a tolerance about ten times the worst benign drift. So at sensible tolerances the margin is saved work, not a worse model.
Other results from the same programme, all with the code in the repository: against a coalition sharing one cheap trajectory the deterring stake does not fall with the number of workers (140 brute-force cells); an agreement term between redundant workers is worth nothing beyond an audit once copying is excluded (0 of 1,349 instances); and a simple predictor of the skip damage misses by 3x to 100x, which refutes our own hypothesis. One dataset and one small model, so these are model checks, not a general law.
The paper skeleton, log and code: research/verifiable-training-mechanisms/.