AI referee report

The central observable object is not defined operationally in the main text. The definition says that ell_i(x) and h_j(x) are "obtained from the corresponding conditional instrument contrasts," but the actual four conditional probabilities and their signs appear only deep in the proof. A reader therefore cannot reconstruct the capacity vector, check its observable implications, or implement the estimator from the definition that every subsequent theorem invokes.

The dedicated literature section identifies the relevant strands but gives the closest competing IV ordinal-benefit result, Gabriel–Sachs–Jensen, only a brief descriptive mention. It likewise summarizes Dong–Heiler without comparing their identified objects, observable inputs, sharpness arguments, and inferential conditions theorem by theorem. Because existing work already supplies response-function IV bounds for finite ordinal outcomes and selected-complier distributional bounds, the current prose leaves the incremental novelty insufficiently adjudicated.

The manuscript is organized around a large inventory of theorem-interface objects rather than the economic argument. Separate definitions of each potential variable are followed by a second system definition; threshold aggregates are defined after their first complete definition; cost objects repeat the algorithm; and the guard-event prose is followed by a formal definition saying only "all guard-event indices." This repetition obscures the short conceptual chain from observed IV contrasts to capacities, transport, sharp bounds, and inference.

The claimed linear-time algorithm is supported by the verified theorem, but the displayed construction is not reproducible as an algorithmic specification. Phrases such as "construct a maximum subflow" and "allocate the residual mass" omit the ordering, tie rules, pointer updates, stopping conditions, and residual invariants that later carry the complexity and optimality argument.

The finite-sample guard is mathematically valid, but its headline placement gives it similar prominence to the sharp identification theorem even though the paper's own calculation shows that the reported set remains [0,1] at remotely realistic sample sizes in the smallest model configuration. The practically informative inferential result presently delivered is the fixed-law directional limit, while the face-aware multiplier object is diagnostic and the uniform guard is best interpreted as an existence or fallback guarantee.

The sentence "The same construction gives sparse endpoint witnesses computable in O(|X|K) operations" is ambiguous after the preceding claim about endpoint-attaining full latent laws. The verified sparsity bound applies to the cellwise coupling traces, while the full latent-law witnesses have no stated global sparsity bound.

The displayed Direction margin assumption states only |Delta q(x)| >= kappa_sigma; strict positivity of kappa_sigma appears afterward in prose. As the manuscript itself observes, the displayed condition becomes vacuous for a nonpositive margin, so the formal environment does not contain the condition attributed to it.

The slate-benefit system definition writes the observed element as O=(X,Z,D,S,SY), whereas the earlier observed-law definition and the formal observed-data type use a missing-value outcome tilde Y. Multiplication by S ordinarily zero-codes an unselected outcome and is not equivalent to an explicit missing marker when zero is an outcome level.

The sentence describing C_{1-alpha,n} as "the guarded interval constructed from the finite face diagnostic" conflicts with the earlier and verified construction: the interval is determined by the plug-in endpoints and deterministic padding, while the multiplier face envelope is reported separately and has no role in coverage.

The projection step is presented mainly as estimator construction, while its model-diagnostic meaning receives little attention. At the population law, capacity nonnegativity is an observable implication of the maintained IV and monotonicity restrictions; in samples, coordinatewise projection can conceal sizable raw violations.

The partial-transport characterization is cited chiefly to a general optimal-transport reference, although the available literature includes work specifically on partial transport and mass-constrained couplings. The current citation support is broader than the precise mathematical device being invoked.

Sample indexing alternates between O_1,...,O_n and sums over r=0,...,n-1. The empirical-cell and empirical-frequency definitions therefore use a convention different from the sampling assumption, multiplier process, and surrounding prose.

The title "No-selection reduction" carries an unexplained asterisk even though the theorem-local formalization-scope footnote already records the published input.