Why it is a question
THEORY-318 now states what the Supplementary Material of LIT-964 proves and the record has re-derived: a bound k on the max-information between a dataset and an analyst’s chosen statistic multiplies the chance that the statistic overfits by at most 2^k, and ε-differential privacy keeps k at most log₂e·εn. That bound alone needs ε of order τ² over the whole interaction, too strict to reuse a holdout at useful sizes. Reuse rests on the sharper transfer theorems (Theorems 6 and 8), on Thresholdout’s privacy (Lemma 10), and on its accuracy guarantee (Theorem 11), whose proofs are in the companion papers (arXiv:1411.2664, arXiv:1506.02629). NOTE-848 read their statements, not their proofs, and the Science main text was not reached.
What would answer it
A reading of the proofs of Theorems 6, 8 and 11 and Lemma 10 in the companion papers, confirming the bounds as stated, would answer it yes. An ε-differentially private mechanism and an adaptive analyst for which the chosen statistic’s empirical mean exceeds its true mean by τ with probability above the stated bound would answer it no. Simulations in which a reused holdout does or does not overfit cannot settle it: the claim is a worst case over all analysts, and the simulated implementation is not the analysed algorithm.