{"paper":{"title":"A Note on the Folding Test of Unimodality: limitation and improved alternative","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The folding test of unimodality misclassifies certain multimodal mixtures as unimodal, but a double-folding version corrects the error.","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Anne M. Ruiz, Aurore Archimbaud, Colombe Becquart, Zaineb Smida","submitted_at":"2026-05-13T10:40:11Z","abstract_excerpt":"This note addresses a key limitation of the Folding Test of Unimodality (FTU). In specific univariate mixture settings, the folding-based criterion can systematically fail, misclassifying clearly multimodal distributions as unimodal. We fully characterize these failures for Dirac mixtures and extend the analysis to Gaussian mixtures. We then introduce a double-folding procedure that captures complementary information, leading to a new test, the Double Folding Test of Unimodality. It resolves the FTU failures and improves multimodality detection power in simulations."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"the folding-based criterion can systematically fail, misclassifying clearly multimodal distributions as unimodal. We fully characterize these failures for Dirac mixtures and extend the analysis to Gaussian mixtures. We then introduce a double-folding procedure that captures complementary information, leading to a new test, the Double Folding Test of Unimodality. It resolves the FTU failures and improves multimodality detection power in simulations.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That applying the folding operation twice captures complementary information about modality without introducing new biases or reducing detection power in non-mixture or other distribution settings.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The Double Folding Test of Unimodality resolves systematic failures of the original FTU on Dirac and Gaussian mixtures and enhances multimodality detection.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The folding test of unimodality misclassifies certain multimodal mixtures as unimodal, but a double-folding version corrects the error.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"58b34b7ff408821ca71c0326ac39e197170213aabe69447a0eceb82a4ad8bb9b"},"source":{"id":"2605.13326","kind":"arxiv","version":1},"verdict":{"id":"f560fc36-47df-4b91-931d-6a1c3adf9eb3","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:08:03.080870Z","strongest_claim":"the folding-based criterion can systematically fail, misclassifying clearly multimodal distributions as unimodal. We fully characterize these failures for Dirac mixtures and extend the analysis to Gaussian mixtures. We then introduce a double-folding procedure that captures complementary information, leading to a new test, the Double Folding Test of Unimodality. It resolves the FTU failures and improves multimodality detection power in simulations.","one_line_summary":"The Double Folding Test of Unimodality resolves systematic failures of the original FTU on Dirac and Gaussian mixtures and enhances multimodality detection.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That applying the folding operation twice captures complementary information about modality without introducing new biases or reducing detection power in non-mixture or other distribution settings.","pith_extraction_headline":"The folding test of unimodality misclassifies certain multimodal mixtures as unimodal, but a double-folding version corrects the error."},"references":{"count":24,"sample":[{"doi":"","year":1985,"title":"The annals of Statistics , pages=","work_id":"4f9c6967-a4d4-49a1-ad5f-cace29b48f52","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Are your data gathered? , abstract =","work_id":"96091fc6-31a5-4b65-809a-e31c8f7356b0","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"New statistical methods for data mining, contributions to anomaly detection and unimodality testing , copyright =","work_id":"edce8f3d-e101-42b5-b45f-025606de6200","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"arXiv preprint arXiv:2311.16614 , author =","work_id":"dd9a4913-eb0b-49f1-8cfe-9997244be76f","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1981,"title":"Journal of the Royal Statistical Society Series B: Statistical Methodology , author =","work_id":"b953a2d9-e38e-48c3-80aa-1593d5176451","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":24,"snapshot_sha256":"49ba3d212dde7b784587603d9ab17a957ed2d087f9d876d5a2a5802c42e5b4c9","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}