R3 and R4 note that assumption 2--the embedding method extracts the salient predictive information

We thank the reviewers for reading the paper and for their detailed comments. However, establishing such results is outside the scope of the paper. R3 and R4 both note that partially correcting for confounding may hurt. We have corrected the typos you point out (1. is anonymized ref, 2. is estimate of all nuisance params, 3. is sigmoid) We agree; this was a minor error on our part. Beyond the fact that it fixes the bug, we think this condition is more interpretable--thank you!