{"id":"856dfa7b-d090-41cb-a25c-01cad42987a8","arxiv_id":"2603.24792","paper_version":3,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Online e-closure and donation-based compound e-values strictly improve power of online FDR procedures under arbitrary dependence, with O(log t) decisions.","lead":"This paper proposes faster, more powerful ways to control false discoveries when hypotheses arrive one after another in a stream. It matters for any field that tests many claims continuously—genomics, A/B testing, finance—where dependence between tests is messy and power is scarce.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.5","headline":"Abstract-only review: the load-bearing validity of online e-closure and donation-based compound e-values under arbitrary dependence cannot be checked, so the central claim remains uninspectable.","rationale":"The Reader correctly flags that the martingale/e-process validity of the two online constructions is the load-bearing assumption and that it is only asserted in the abstract. With no full text, proofs, algorithms or experiments available, that assumption cannot be stress-tested further; manufacturing a more specific algebraic flaw would violate the good-faith rule. The appropriate posture is therefore to leave the verdict UNVERDICTED and the confidence LOW, exactly as the Reader did. The concrete test simply operationalizes the missing check: once the paper is in hand, inspect the FDR theorem for a clean reduction to a valid e-process. Agreement with the Reader is complete on both the identity of the weakest link and the resulting verdict.","tokens_in":1917,"tokens_out":512,"duration_ms":5407,"concrete_test":"Obtain the full preprint (or arXiv source). Locate the theorem that states FDR control for the online e-closure / donation compound-e procedure under arbitrary dependence. Verify that its proof reduces the online construction to a valid e-process (or closed testing) argument without an extra independence or boundedness assumption that is not present in the classical offline case. If the reduction fails or introduces such an assumption, the central claim does not hold as stated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The strongest claim requires that the online e-closure principle and the donation-defined online compound e-values preserve the supermartingale / e-process properties that deliver FDR control under arbitrary dependence in a fully sequential stream, while still producing strictly more rejections than existing e-value and p-value online FDR procedures. Because only the abstract is available, neither the formal definitions of the online analogs, the donation accounting, nor any theorem establishing that the resulting processes remain valid e-processes (or that the online e-closure still controls FDR) can be examined. The O(log t) claim and the empirical gains are likewise uninspectable. This is not a manufactured inconsistency; it is simply that the single condition on which both the power improvement and the FDR guarantee rest is asserted rather than exhibited. Consequently no technical soft spot inside the argument can be confirmed or refuted from the given material.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The manuscript (available here only as an abstract) proposes a framework for online multiple testing with FDR control under arbitrary dependence. It introduces two constructions: an online analog of the e-closure principle, and online compound e-values defined via a donation mechanism. The authors claim these yield strict power improvements over state-of-the-art e-value and p-value online FDR procedures while retaining FDR control, that decisions at time t can be computed in O(log t) time, and that the methods show improved empirical performance on synthetic and real data.","tokens_in":2121,"tokens_out":713,"duration_ms":16412,"significance":"If the claims hold as stated, the work would be a meaningful contribution to online FDR methodology. Strict power gains that preserve validity under arbitrary dependence in a fully sequential stream are practically relevant, and an O(log t) decision algorithm would address a genuine computational bottleneck. The dual constructions (online e-closure and donation-based compound e-values) are of independent methodological interest. These strengths cannot be confirmed from the abstract alone; formal definitions, theorems, algorithms, and empirical design are required for a full assessment.","major_comments":[{"comment":"Abstract: The load-bearing claim is that the online e-closure principle and donation-defined online compound e-values preserve the supermartingale / e-process properties needed for FDR control under arbitrary dependence in a fully sequential streaming model, while still producing strictly more rejections than existing procedures. This validity is asserted rather than exhibited: no formal definitions, theorem statements, or proof sketches appear in the available text. Without those, neither the FDR guarantee nor the strict-power claim can be checked.","section":null},{"comment":"Abstract: The claim of 'strict power improvements over state-of-the-art e-value and p-value procedures' is not accompanied by a precise statement of which procedures are dominated, under what conditions the improvement is strict, or any dominance theorem. That comparison is central to the contribution and remains uninspectable from the abstract.","section":null},{"comment":"Abstract: The O(log t) decision algorithm and the reported empirical gains on synthetic and real data are likewise uninspectable. Algorithmic description, complexity analysis, simulation design, data sources, and quantitative results are all absent from the available text, so these supporting claims cannot be evaluated.","section":null}],"minor_comments":[{"comment":"Abstract: The phrase 'online analogs of e-closure and compound e-values' is used without even a one-sentence informal definition of either object; a brief clarifying clause would help readers orient before the full paper.","section":null},{"comment":"Abstract: 'Donations' is introduced as the defining mechanism for online compound e-values without any indication of what is being donated or how the accounting works; a short parenthetical would reduce ambiguity.","section":null}],"recommendation":"uncertain","confidential_remarks":"Only the abstract was available for this review (full text not provided). A proper technical assessment of FDR validity, power dominance, complexity, and empirics is impossible without the manuscript body. I recommend that the editor either supply the full paper for re-review or treat this as an incomplete submission until the full text is in hand. My recommendation of 'uncertain' reflects that limitation, not a judgment that the claims are false."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The one thing to know is that this abstract claims a clean methodological advance for online FDR under arbitrary dependence: an online e-closure principle plus a donation-based definition of online compound e-values, with strict power gains over current e- and p-value procedures, O(log t) decisions, and some empirical wins. That package would matter if it holds.\n\nWhat looks new is the packaging. Online e-closure and the donation construction for compound e-values are presented as the levers that let them improve on named SOTA methods without giving up FDR under arbitrary dependence. The O(log t) claim is also concrete and useful if the algorithms are real. The abstract is clear about the target setting (streaming hypotheses, continuous testing) and does not hide behind vague language.\n\nThe soft spot is simply that we only have the abstract. The load-bearing piece is whether the online analogs still give valid e-processes or supermartingales so that FDR control survives the sequential stream and the power improvement is not free. That is asserted, not shown. Same for the algorithms and the experiments. I am not inventing a flaw in the argument; I cannot inspect the argument. The reader and stress-test are right that confidence has to stay low until the definitions and theorems are visible. Nothing in the abstract smells circular or tautological; the residual risk is ordinary “does the construction actually work.”\n\nThis is for people who already care about online multiple testing, e-values, and sequential FDR. A methods reader in that corner gets value from the framing even before the proofs. It deserves a serious referee once the full text is in hand; the problem is real and the claimed tools are specific enough that desk rejection would be premature. I would not cite it yet and would not put an abstract-only piece in reading group, but I would accept it for peer review and read the paper when it appears.","headline":"Abstract-only: promising online FDR tools via e-closure and donation compound e-values, but validity and power claims are uncheckable without the paper.","tokens_in":2728,"tokens_out":481,"would_cite":false,"duration_ms":5364,"reading_group":"no","serious_thinker":"unclear","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62H15","62L10"],"pacs":[],"model":"grok-4.5","headline":"Online e-closure and donation-based compound e-values give strict power gains for sequential FDR control under arbitrary dependence.","keywords":["online FDR","e-values","e-closure principle","compound e-values","sequential multiple testing","arbitrary dependence","donation mechanism"],"falsifier":"Construct a sequential stream of dependent e-values (or p-values) on which an existing state-of-the-art online FDR procedure rejects a strict superset of the discoveries produced by the new methods, or on which the new methods exceed the target FDR level.","tokens_in":2783,"feed_emoji":"📈","tokens_out":552,"duration_ms":6189,"temperature":0.7,"pith_summary":"When hypotheses arrive continuously in a stream and must be tested online with false discovery rate control, standard e-value and p-value procedures leave power on the table. This paper shows that two online analogs of classical ideas—the e-closure principle and compound e-values built by a donation mechanism—recover that power while still guaranteeing FDR control under arbitrary dependence among the tests. Decisions remain computable in logarithmic time in the number of hypotheses seen so far. A sympathetic reader cares because many modern scientific pipelines (genomics, A/B testing platforms, continuous monitoring) are inherently sequential; any method that raises power without sacrificing validity or speed directly increases the number of true discoveries that can be reported with the same error guarantee.","feed_headline":"Online e-closure lifts power for sequential FDR control","feed_subtitle":"Donation-based compound e-values beat state-of-the-art methods under arbitrary dependence, in log time","key_machinery":"Online e-closure (the sequential analog of the classical e-closure principle) and donation-based online compound e-values: the former closes the family of admissible rejection rules online, while the latter lets later tests inherit unused e-value mass from earlier ones, producing the power gain under the same supermartingale validity conditions.","core_discovery":"The online e-closure principle, together with a novel formulation of online compound e-values defined through donations, yields strict power improvements over state-of-the-art e-value and p-value online FDR procedures while retaining FDR control under arbitrary dependence, with decisions computable in O(log t) time at step t.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Online e-closure plus donations lift sequential FDR power","Donation compound e-values beat SOTA online FDR methods","E-closure yields stricter online FDR control under dependence","Power gains for stream FDR via online e-closure principle","Log-time online FDR improved by e-closure and donations"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"That the online versions of e-closure and of donation-defined compound e-values still form valid e-processes (or supermartingales) under arbitrary dependence, so the FDR guarantee carries over from the offline theory.","fun_headline_variants_meta":{"raw":{"variants":["Online e-closure plus donations lift sequential FDR power","Donation compound e-values beat SOTA online FDR methods","E-closure yields stricter online FDR control under dependence","Power gains for stream FDR via online e-closure principle","Log-time online FDR improved by e-closure and donations"]},"model":"grok-4.5","effort":"low","cost_usd":0.00384,"raw_usage":{"total_tokens":1076,"prompt_tokens":654,"num_sources_used":0,"completion_tokens":63,"cost_in_usd_ticks":38400000,"prompt_tokens_details":{"text_tokens":654,"audio_tokens":0,"image_tokens":0,"cached_tokens":0},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":359,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":654,"tokens_out":63,"duration_ms":3441,"temperature":1.0,"reasoning_tokens":359,"cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-13T18:37:04.562011+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Construct a sequential stream of dependent e-values (or p-values) on which an existing state-of-the-art online FDR procedure rejects a strict superset of the discoveries produced by the new methods, or on which the new methods exceed the target FDR level.","supporting_citations":[],"review_version":1}