{"id":"77946e48-e1e0-4009-925e-4ac1b2c6f384","arxiv_id":"2606.07466","paper_version":2,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Covariance-adaptive residualization plus stagewise step-down calibration yields an admissible multiple-testing procedure that often beats marginal methods under arbitrary Gaussian dependence.","lead":"The paper proposes a multiple-testing procedure for Gaussian means that residualizes using the full covariance and calibrates thresholds stagewise. It claims better error control and signal recovery than standard marginal methods under arbitrary dependence.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified: full text is a mismatched manuscript, so the multiple-testing claims cannot be stress-tested.","rationale":"The reader already correctly diagnosed the mismatch (abstract of 2606.07466 vs. full text of 2606.07467), set UNVERDICTED with LOW confidence, and flagged that formal assumptions and simulations are unverifiable. My second-pass inspection of the supplied \"full manuscript\" confirms it is entirely the inflation paper (EFT of dark energy, Mukhanov-Sasaki sources, Horndeski examples, etc.). No multiple-testing content exists to attack or defend. Consequently the verdict remains UNVERDICTED; agreement with the reader is complete. The only useful next step is to obtain the correct manuscript.","tokens_in":26368,"tokens_out":412,"duration_ms":4038,"concrete_test":"Replace the cached full-text block with the actual PDF/source of arXiv:2606.07466; re-run the review on the true residual statistics, active-precision representation, and simulation tables. Only then can the Gaussian/known-covariance assumption and the reported risk/FDR claims be checked.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The CACHEABLE PAPER SOURCE CONTEXT and FULL TEXT block contain the complete manuscript of arXiv:2606.07467 (\"Stochastic scalar-tensor inflation and beyond\" by Launay), not arXiv:2606.07466. No theorems, residual definitions, precision-matrix identities, admissibility arguments, or simulation tables from the multiple-testing paper are present. The reader's strongest claim (admissibility via Ghosh-Chakrabarti + superior FDR/FNR/power under arbitrary covariance) and weakest assumption (joint Gaussianity with usable covariance) therefore cannot be audited against actual equations or results. There is no load-bearing technical soft spot that can be isolated inside the supplied text; any critique would be pure speculation about an unseen paper.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The abstract claims a multiple-testing procedure for multivariate Gaussian means under arbitrary covariance: it keeps the covariance-adaptive residualization of Cohen et al.’s Maximum Residual Down (MRD) method, replaces MRD’s model-dependent thresholds by stagewise critical constants from Gavrilov et al., asserts admissibility by membership in the monotone residual-based step-down class of Ghosh and Chakrabarti (2026), derives an active-precision-matrix representation of the residuals that reduces computation, and reports simulations in which the method often has lower normalized misclassification risk than marginal procedures and, under structured dependence, simultaneously near-nominal FDR, very small FNR, power near one, and rejections near the true signal count. The supplied full-text block, however, is not that manuscript: it is the complete gr-qc paper arXiv:2606.07467 (“Stochastic scalar-tensor inflation and beyond”), with no theorems, residual definitions, precision-matrix identities, admissibility arguments, or simulation tables for the multiple-testing claims.","tokens_in":26495,"tokens_out":918,"duration_ms":14205,"significance":"If the abstract’s claims were substantiated in a matching manuscript, the work would be of clear interest in large-scale dependent testing: a covariance-adaptive residual step-down with a simple calibration rule, an admissibility link to a general monotone class, a computational reduction via active precision geometry, and strong finite-sample recovery under structured dependence would be useful contributions. Those strengths cannot be credited or audited from the material provided, because the body of the submission is a different paper in a different field.","major_comments":[{"comment":"Title/abstract vs. full text: the abstract and paper_id identify a stat.ME multiple-testing paper (MRD residualization, Gavrilov stagewise constants, Ghosh–Chakrabarti admissibility, active precision matrix, FDR/FNR/power simulations). The full manuscript text is instead Launay’s gr-qc paper on stochastic scalar-tensor inflation (EFToDE, Mukhanov–Sasaki sources, Horndeski/EGB examples). No equation, section, table, or proof from the claimed paper is present. The central claims therefore cannot be checked for correctness, and the submission as supplied is not reviewable as the stated work.","section":null},{"comment":"Admissibility (abstract): the abstract states that admissibility “follows directly” from membership in the monotone residual-based step-down class of Ghosh and Chakrabarti (2026). That reference shares year and (per the reader’s note) authorship with the present work. Without the actual definitions, class membership proof, and error-rate control arguments, it is impossible to verify that the construction is not circular or that the cited general theory applies under the paper’s residual and calibration choices.","section":null},{"comment":"Gaussianity and known/usable covariance (abstract): performance and residualization are stated for multivariate Gaussian means under arbitrary covariance, with residuals tied to an active precision matrix. The formal assumptions, estimation of dependence, and robustness when covariance is misspecified or non-Gaussian are not available in the supplied text, so the load-bearing conditions for FDR control and the reported simulation superiority cannot be assessed.","section":null}],"minor_comments":[{"comment":"Once the correct full manuscript is supplied, the abstract’s simulation claims (normalized misclassification risk, simultaneous FDR/FNR/power/rejection counts under structured dependence) will need to be tied to explicit tables, dependence models, and competitors; those materials are absent here.","section":null},{"comment":"The abstract’s “alternative representations … through a single active precision matrix” should be matched to numbered identities and complexity statements in the correct paper; they cannot be located in the gr-qc text provided.","section":null}],"recommendation":"uncertain","confidential_remarks":"The review packet is broken: abstract and arXiv id point to 2606.07466 (stat.ME), while the full-text block is 2606.07467 (gr-qc). I cannot produce a scientific accept/revise/reject decision on the multiple-testing claims. Please re-supply the correct PDF/source for 2606.07466 (or confirm intentional abstract-only review). Until then the only honest recommendation is uncertain."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The only usable material for 2606.07466 is the abstract. The cacheable full-text block is Launay’s stochastic scalar-tensor inflation paper (2606.07467). So we have no theorems, residual definitions, precision-matrix identities, proofs, or simulation tables for the multiple-testing work. That is the whole story for this pass.\n\nWhat the abstract promises is coherent and potentially useful: keep Cohen et al.’s MRD residualization under arbitrary covariance, replace the original model-dependent thresholds with Gavrilov-style stagewise constants, claim membership in the monotone residual-based step-down class of Ghosh & Chakrabarti (2026) so admissibility is free, rewrite the active residuals via a single active precision matrix for cheaper computation, and report strong simulation gains in normalized misclassification risk plus near-ideal FDR/FNR/power under structured dependence. If those pieces check out, this is a clean, practical advance inside dependent Gaussian multiple testing.\n\nSoft spots are exactly the ones you cannot check without the real manuscript. Admissibility is asserted by citation to a same-author 2026 paper; that may be fine if the membership is immediate, but it is a self-citation chain we cannot inspect. The Gaussian + usable-covariance assumption is load-bearing for residualization and for the simulation claims; without the text we cannot see how estimation error or non-Gaussianity is handled. The “remarkably strong signal-recovery” language is strong; it needs the tables.\n\nThis is for people who already work on residual-based or covariance-aware multiple testing and want an admissible stagewise rule that actually uses the precision matrix. It is not a foundational rewrite of the field. Because the abstract is clear and the claimed combination is non-trivial, a serious editor should send the real paper to referees rather than desk-reject. I would not cite or bring it to reading group until the correct PDF is in hand. Once it is, the first things to verify are the precision-matrix residual rewrite, the exact membership argument for admissibility, and whether the simulations control FDR under estimated rather than oracle covariance.","headline":"Abstract-only multiple-testing claim; the supplied full text is a different gr-qc paper, so we cannot audit the residual identities, admissibility argument, or simulations.","tokens_in":27130,"tokens_out":520,"would_cite":false,"duration_ms":5888,"reading_group":"no","serious_thinker":"unclear","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62H15","62J15"],"pacs":[],"model":"grok-4.5","headline":"Covariance-adaptive residual testing with stagewise critical values controls dependent multiple tests and recovers signals more cleanly than marginal methods.","keywords":["multiple testing","covariance-adaptive residualization","stagewise calibration","MRD","precision matrix","FDR","Gaussian means","dependent tests"],"falsifier":"Under a non-Gaussian multivariate law, or with badly misspecified covariance, check whether the procedure still keeps FDR near the nominal level while matching or beating marginal competitors on normalized misclassification risk and signal recovery; systematic failure would overturn the performance claims.","tokens_in":27231,"feed_emoji":"📐","tokens_out":620,"duration_ms":5443,"temperature":0.7,"pith_summary":"When many means are tested at once and the observations share an arbitrary covariance structure, ordinary marginal p-values waste the dependence information. This paper keeps the Maximum Residual Down residualization idea of Cohen et al. but replaces its model-specific thresholds with the generalized step-down constants of Gavrilov et al., producing a simple, covariance-adaptive step-down rule. The resulting procedure is monotone residual-based, so earlier admissibility theory applies at once. The same residuals can be rewritten through a single active precision matrix, which both cuts computation and shows that residualization is geometry of the precision matrix restricted to the still-active coordinates. Simulations across many dependence patterns show lower normalized misclassification risk than popular marginal competitors; under several structured covariances the method simultaneously keeps FDR near the target, drives FNR nearly to zero, pushes power near one, and rejects roughly the true number of signals. Dependence is therefore not merely a nuisance: residualization plus stagewise calibration can turn it into a tool for cleaner large-scale inference.","feed_headline":"Residual tests turn dependence into better multiple testing","feed_subtitle":"Stagewise calibration plus active precision matrices recover signals while keeping FDR near target","key_machinery":"Covariance-adaptive residual statistics of the MRD type, re-expressed through one active precision matrix and calibrated by Gavrilov et al. generalized step-down critical constants; the construction places the rule inside the monotone residual-based step-down class whose admissibility is already known.","core_discovery":"A stagewise-calibrated version of Maximum Residual Down residualization yields an admissible, covariance-adaptive step-down procedure for multivariate Gaussian means under arbitrary dependence; the residuals admit a single active-precision-matrix representation, and the resulting tests frequently dominate marginal methods on normalized misclassification risk while recovering nearly all signals under structured dependence.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Stagewise residualization cuts risk under arbitrary dependence","Active precision matrices simplify admissible residual step-down tests","Covariance-adaptive residuals beat marginal methods on misclassification","Stagewise-calibrated MRD recovers nearly all signals near FDR target","Single active precision matrix yields faster residual multiple testing"],"cache_read_input_tokens":16512,"weakest_assumption_plain":"The data are jointly Gaussian and the covariance (or its precision matrix) is known well enough that the residual statistics and their stagewise thresholds remain valid.","fun_headline_variants_meta":{"raw":{"variants":["Stagewise residualization cuts risk under arbitrary dependence","Active precision matrices simplify admissible residual step-down tests","Covariance-adaptive residuals beat marginal methods on misclassification","Stagewise-calibrated MRD recovers nearly all signals near FDR target","Single active precision matrix yields faster residual multiple testing"]},"model":"grok-4.5","effort":"low","cost_usd":0.005076,"raw_usage":{"total_tokens":1444,"prompt_tokens":801,"num_sources_used":0,"completion_tokens":61,"cost_in_usd_ticks":50760000,"prompt_tokens_details":{"text_tokens":801,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":582,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":801,"tokens_out":61,"duration_ms":4363,"temperature":1.0,"reasoning_tokens":582,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-12T14:49:26.855900+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Under a non-Gaussian multivariate law, or with badly misspecified covariance, check whether the procedure still keeps FDR near the nominal level while matching or beating marginal competitors on normalized misclassification risk and signal recovery; systematic failure would overturn the performance claims.","supporting_citations":[],"review_version":2}