AI referee report

The principal frontier statements appear near the end of the supplied-propensity appendix, although the main text repeatedly announces an immediately forthcoming result. For example, 'The next result gives matching bounds for the broader-class critical radius' is followed by interpretation rather than the theorem. The same problem affects the heavy-tail comparison, the shared-class oracle frontier, and the preservation boundary. Readers must traverse extensive construction details and appendices to locate the formal answers to the paper's main questions.

Repeated definitions and repeated explanatory summaries obscure the logical progression. The heterogeneity distance, model suprema, public domains, experiment, and rejection expectation are reintroduced across numerous environments and their surrounding paragraphs. The calibration and mean handles also restate much of the already specified algorithm, while several paragraphs repeat the same size, power-gate, and capping interpretations.

Several ordinary-prose passages violate the affirmative-scope contract. These include 'it does not replace the variance by a fold-specific proxy or assume a learned first stage,' 'Requirements for a particular estimated-propensity procedure are outside this experiment comparison,' and the statement that practical calibration requires implementation and simulation 'beyond the present analysis.' The last two identify genuine extension or non-coverage content outside the expressly titled limitations subsection.

The explanation that 'propensity regularity enters twice through treatment weighting and projection correction, whereas the baseline appears once and is amplified by the tail factor' assigns a precise mechanism to individual denominator terms without displaying the scalar balance that supports that interpretation. The verified statements establish the exponent and covariance bounds; readers need a clearer bridge between those bounds and this explanation.

The higher-order CATE paragraph identifies the methodological connection and different loss criterion, but its comparison remains qualitative despite the cited work's explicit minimax phase transition. This is particularly relevant to the paper's independent propensity and baseline exponents and its quadratic-testing mechanism.

The scientific interpretation centers on the standard deviation of the conditional effect, but the economic reason to care about the two comparisons remains abstract. The introduction gives extensive technical detail before developing a concrete use of a scalar effect modifier or explaining when supplied assignment information corresponds to an economically meaningful design.

The sentence 'The same calculation applies under the zero-based convention after translating the block indices' introduces an unexplained alternative convention after the manuscript has consistently adopted one-based blocks. Terms such as 'retained,' 'handle,' and 'ledger' also recur where standard descriptions would communicate the mathematical role more directly.