AI referee report

The contribution is too narrow for the econometrics framing as written. The paper explicitly says, "we take the objective $F_{r,\kappa }$ as given—a covariance design criterion ... and do not derive it from a specific estimand, estimator, variance, or welfare target," but the title, introduction, and discussion frame the work as a contribution to randomized experiments under interference.

The abstract presents the norm term as a "Schatten–2 robustness penalty" and says iid assignment is an "asymptotic target as the robustness weight diverges." The verified layer proves facts about a Schatten–2 norm penalty; it does not establish statistical robustness, minimax robustness, robustness to graph misspecification, or robustness of inference.

The paper repeatedly draws design-practice implications that exceed the formal scope. For example, "For interference-aware randomized design, the practical implication is that solving the covariance relaxation is not by itself enough" is true only for this two-block, sign-symmetric, block-exchangeable, no-fixed-count criterion, not for interference-aware randomized design generally.

The novelty claim around the parity-truncated characterization is under-supported. The discussion says, "We are not aware of a prior statement of this parity-truncated characterization..." but the paper does not engage enough with finite exchangeability, Rademacher moment problems, or low-dimensional correlation-polytope slices to substantiate novelty at journal standard.

The verification note lists Lean version, mathlib revision, namespace, and declaration names, but it does not provide an accessible artifact, build command, or archival identifier. For a paper relying on machine checking, this is insufficient reproducibility information.

The theorem title "Sharp Rounding Loss" is misleading because no rounding algorithm is defined or analyzed. The theorem computes an implementability or truncation loss, not the loss of a specified rounding procedure.

The worked example and Table 1 risk implying a comprehensive phase diagram. The table heading "Regime" can be read as partitioning the parameter space, even though the cut and gap results leave intervals not classified by the named theorems and the paper explicitly disclaims global boundaries.

The sentence "no generality is lost in the benchmark" is easy to overread, even though the next paragraph narrows the claim. The reduction is only for the specific invariant objective and sign-symmetric feasible class.

The label "Balanced Sign Symmetry" and notation ${\mathcal{P}}_m^{\mathrm{bal}}$ invite confusion because the condition does not impose fixed treated counts or exact realized balance.

The scale convention $W_{ij}=a/m,b/m$ and the low-scale condition $a+3b<2m$ are stated but not economically motivated. A reader is left unsure whether $a,b$ are fixed intensities, growing with $m$, or normalized degrees.

The paragraph introducing the active-set ingredients says these objects are "established in Appendix \ref{sec:deferred-proofs} (Lemmas...)" but the lemmas themselves are collected in Appendix A, while \ref{sec:deferred-proofs} labels the later proof-sketch appendix.

The abstract is too dense and uses theorem-local phrases before notation is introduced, such as "the stated low-scale condition" and "the stated robustness range." This makes the contribution hard to parse for readers not already inside the formal development.

Notation alternates between $z_{\mathrm{sp}}$, $z$, and explanations about an "ambient sign index." The truncation lemma also uses $z$ where the main text uses $z_{\mathrm{sp}}$.