{"id":"45e87b9f-3501-41a1-81ad-21f2cf05d7dc","arxiv_id":"2607.01036","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"An algorithm returns an EJR+ committee in the ARRV spatial model using O(d log d k) Planar queries per voter in expectation, independent of candidate count, for any distribution over rectangular preferences when the electorate is large enough.","lead":"The paper gives an algorithm that returns a committee satisfying the strong fairness property EJR+ while asking each voter only O(d log d k) simple comparison queries about their preferences in a spatial model. This matters for large elections such as participatory budgeting because it reduces the information burden on voters without losing the proportional-representation guarantee.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"Modules supplied only for known/unknown/smooth distributions, not arbitrary ones claimed in the central result","rationale":"Reader correctly flags the large-electorate assumption as load-bearing but does not address the narrower scope of the modules; the distribution-class restriction is an independent and equally critical precondition for the O(d log d k) bound to hold for arbitrary preferences.","tokens_in":1720,"tokens_out":296,"duration_ms":10185,"concrete_test":"Locate the module constructions (likely §4–5) and test whether they apply to an arbitrary distribution that is neither known a priori, nor falls under the paper’s definition of “unknown,” nor satisfies the smoothness condition; if every construction invokes one of those three restrictions, replace the claim “any distribution” with the restricted classes actually handled.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The strongest claim asserts an algorithm that returns an EJR+ committee for *any* distribution over ARRV preferences with the stated query bound. The verify-or-fallback framework requires interchangeable modules that each supply two specific properties (presumably a verification test and a fallback sampler whose costs yield the O(d log d k) bound). The abstract states that such modules are described only for the restricted classes “known, unknown, and smooth distributions.” For a distribution outside these classes the required properties may not be realizable with cost independent of m, violating the headline guarantee.","agreement_with_reader":"partial"},"referee_report":null,"author_rebuttal":null,"desk_editor":null,"rs_alignment":null,"lean_confirmation":null,"pith_extraction":null,"created_at":"2026-07-02T04:02:43.248924+00:00","model_set":{"reader":"grok-4.3"},"falsifier":null,"supporting_citations":[],"review_version":1}