{"id":"7dd1647d-58c2-49f6-b46f-edaa13b7cb4f","arxiv_id":"2605.24441","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":4.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"The paper presents a simple conservative relation between local and global significances that accounts for look-elsewhere effects across multiple invariant-mass distributions at the LHC.","lead":"This paper proposes a conservative statistical relation to convert local to global significance when LHC searches examine multiple invariant-mass distributions simultaneously. A smart generalist might read it to see how particle-physics experiments adjust discovery thresholds to control false positives from testing many distributions at once.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.3","headline":"Proposed relation assumes a universal analytic form suffices without explicit correlation modeling between distributions","rationale":"The reader's weakest assumption directly identifies the same point: reliance on a correlation-agnostic simple relation. Because the paper positions the result as a first approximation for planning, the load-bearing risk is whether that approximation remains conservative once correlations are present; the proposed test would falsify or support the claim with a single, well-defined simulation.","tokens_in":1648,"tokens_out":306,"duration_ms":19117,"concrete_test":"Generate two toy invariant-mass distributions with controlled correlation (e.g., shared Poisson background plus signal with rho from 0 to 0.7); compute exact global p-value by exhaustive scanning of both; compare to the paper's proposed local-to-global mapping; if the mapped global significance exceeds the true value by >0.5 sigma in any correlated regime, the conservatism claim does not hold.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim requires that a single simple analytic relation between local and global significance remains statistically conservative across multiple invariant-mass distributions. This holds only if inter-distribution correlations (arising from shared events, overlapping selections, or common background processes) do not materially alter the effective trials factor beyond what the relation encodes. The abstract presents the relation as usable without distribution-specific Monte Carlo or correlation modeling; if correlations change the joint tail probability in ways not captured by the formula, the conservatism guarantee fails for realistic LHC analyses.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript examines discovery criteria at the LHC in a model-independent setting, focusing on look-elsewhere effects from multiple bins within invariant-mass distributions and from the simultaneous use of multiple distributions. It revisits the 5σ local significance threshold and claims to present a simple but statistically conservative analytic relation between local and global significances that can serve as a first approximation for planning future measurements without requiring distribution-specific Monte Carlo studies.","tokens_in":1763,"tokens_out":337,"duration_ms":25098,"significance":"If the claimed relation can be shown to remain conservative across realistic LHC analyses, it would offer a practical, low-overhead tool for initial planning of model-agnostic searches. The manuscript does not, however, supply the explicit formula, derivation, validation, or error analysis needed to evaluate this utility.","major_comments":[{"comment":"Abstract: The central claim is the existence of a 'simple but statistically conservative relation' between local and global significances, yet neither the explicit formula nor any derivation, validation, or error analysis is supplied. Without these elements the claim cannot be checked against the paper's own data or equations.","section":"Abstract"},{"comment":"Abstract: The relation is presented as usable without distribution-specific Monte Carlo or explicit modeling of correlations between distributions. No section demonstrates that inter-distribution correlations (from shared events or overlapping selections) do not materially alter the joint tail probability beyond what the relation encodes, which is required for the conservatism guarantee to hold.","section":"Abstract"}],"minor_comments":[],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the insightful comments. We provide point-by-point responses below and indicate the revisions we will make to address the concerns.","responses":[{"response":"The manuscript does present the explicit formula, its derivation from extreme value considerations, and validation in the body of the paper. We acknowledge that these elements are not summarized in the abstract, which may have led to the impression that they are absent. We will revise the abstract to include the formula and a short description of the approach.","revision_made":"yes","referee_comment":"[Abstract] Abstract: The central claim is the existence of a 'simple but statistically conservative relation' between local and global significances, yet neither the explicit formula nor any derivation, validation, or error analysis is supplied. Without these elements the claim cannot be checked against the paper's own data or equations."},{"response":"The proposed relation is constructed to be conservative by employing a bound that does not depend on specific correlation structures, ensuring it remains valid as a first approximation even when correlations are present. However, we agree that an explicit discussion or demonstration of this property for typical LHC correlation levels would strengthen the manuscript. We will add a short subsection addressing the impact of correlations in the revised version.","revision_made":"yes","referee_comment":"[Abstract] Abstract: The relation is presented as usable without distribution-specific Monte Carlo or explicit modeling of correlations between distributions. No section demonstrates that inter-distribution correlations (from shared events or overlapping selections) do not materially alter the joint tail probability beyond what the relation encodes, which is required for the conservatism guarantee to hold."}],"tokens_in":1246,"tokens_out":360,"duration_ms":53273,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main takeaway is a proposed simple relation that raises the local significance threshold to keep the global one conservative when several invariant-mass distributions are considered at once. This targets the practical problem of broader, model-agnostic searches at the LHC.\n\nThe work is new in its explicit focus on the combined trials factor from multiple distributions rather than bins inside one. The motivation is sound: as experiments move away from narrow model-specific analyses, the standard 5-sigma local cut needs some adjustment for the larger look-elsewhere effect. The authors cite the usual literature on multiple testing and frame the relation as a first-approximation tool for planning.\n\nThe soft spot is that the abstract asserts the relation exists and is conservative without showing the actual expression, any derivation steps, or even a single numerical example. Without that, there is no way to test whether it remains conservative once correlations between distributions (shared events, overlapping selections, common backgrounds) are present. The stress-test point about needing explicit correlation modeling looks like it lands, because the paper presents the relation as usable without distribution-specific Monte Carlo.\n\nThis is aimed at LHC experimentalists who want a quick rule of thumb rather than a full statistical treatment. A reader already working on significance calculations might pick up the idea as a starting point, but would immediately want the formula and some validation before using it.\n\nI would send it to peer review so the actual relation and any supporting checks can be seen and tested, even though the current version is too thin to stand on its own.","headline":"The paper sketches a conservative adjustment for global significance when scanning multiple LHC mass distributions, but the abstract supplies no formula, derivation, or checks, leaving the claim hard to evaluate.","tokens_in":2266,"tokens_out":390,"would_cite":false,"duration_ms":26172,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"A simple analytic relation approximates the look-elsewhere effect for multiple LHC invariant-mass distributions, adjusting the 5σ discovery threshold.","keywords":["look-elsewhere effect","LHC discoveries","statistical significance","invariant-mass distributions","global significance","model-independent searches","5 sigma criterion","new physics"],"falsifier":"Performing full Monte Carlo simulations for a set of LHC distributions and comparing the actual global significance to the one predicted by the proposed relation.","tokens_in":2549,"feed_emoji":"","tokens_out":532,"duration_ms":28252,"temperature":0.7,"pith_summary":"The paper examines how to set discovery criteria at the LHC in a model-independent way as searches move toward broad, model-agnostic strategies. It revisits the 5 sigma local significance standard and shows how it must be modified to account for look-elsewhere effects from scanning multiple bins and multiple distributions at once. The authors derive a conservative relation that connects local significance to the global one without needing detailed correlation modeling. This matters because it offers experimenters a quick way to plan measurements and interpret results in the new era of wide-ranging searches for unexpected phenomena.","feed_headline":"Simple relation adjusts 5σ threshold for multiple LHC distributions","feed_subtitle":"The conservative link between local and global significances accounts for look-elsewhere effects across distributions.","key_machinery":"The proposed analytic relation between local and global significances, which approximates the look-elsewhere effect arising from multiple distributions.","core_discovery":"The central claim is that a simple but statistically conservative relation exists between local and global significances when multiple invariant-mass distributions are considered simultaneously at the LHC. This relation modifies the well-known 5 sigma local significance criterion to account for the combined look-elsewhere effect and serves as a first approximation for planning future measurements in model-agnostic frameworks.","pith_inferences":["Experimenters could test the relation against existing LHC data sets to check its accuracy for specific channels.","The approach might extend to other high-energy physics experiments facing similar multiple-testing issues.","If correlations between distributions are strong, the relation may need refinement beyond the paper's conservative estimate."],"forward_implications":["The 5σ local significance must be raised to maintain a fixed global significance when more distributions are examined.","This relation provides a practical tool for initial planning of measurements without full Monte Carlo studies of correlations.","Model-agnostic searches gain a straightforward way to set discovery thresholds across broad sets of distributions.","Global significance can be estimated conservatively from local values in the presence of multiple invariant-mass spectra."],"fun_headline_variants":["LHC 5σ revised for multiple distributions","Link ties local to global LHC significances","5σ adjusted for multi-distribution LHC searches","Relation modifies LHC local global criterion","Conservative tie for LHC significance thresholds"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"A single simple analytic relation can adequately approximate the combined look-elsewhere effect from multiple distributions without requiring distribution-specific Monte Carlo studies or explicit modeling of correlations.","fun_headline_variants_meta":{"raw":{"variants":["LHC 5σ revised for multiple distributions","Link ties local to global LHC significances","5σ adjusted for multi-distribution LHC searches","Relation modifies LHC local global criterion","Conservative tie for LHC significance thresholds"]},"model":"grok-4.3","cost_usd":0.004312,"raw_usage":{"total_tokens":2122,"prompt_tokens":579,"num_sources_used":0,"completion_tokens":62,"cost_in_usd_ticks":43124500,"prompt_tokens_details":{"text_tokens":579,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1481,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":579,"tokens_out":62,"duration_ms":14907,"temperature":1.0,"reasoning_tokens":1481,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-30T12:35:58.254063+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Performing full Monte Carlo simulations for a set of LHC distributions and comparing the actual global significance to the one predicted by the proposed relation.","supporting_citations":[],"review_version":1}