{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:QBDYUQWWCJV4ZGSYN5ZRLTF2PN","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"370993d3ab16aa30fbad6235be5219e44fccec73cca7568b815f82b43a90edc4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-05-13T10:40:11Z","title_canon_sha256":"272bf61f58f668f1dc5d11c667a13a577ea5447a6ccab46681c3704624c2a075"},"schema_version":"1.0","source":{"id":"2605.13326","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.13326","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"arxiv_version","alias_value":"2605.13326v1","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13326","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"pith_short_12","alias_value":"QBDYUQWWCJV4","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"QBDYUQWWCJV4ZGSY","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"QBDYUQWW","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:b4fb9b40ac7bfaf229489a06449a56f28da9eafa4046fb1b7b7fe6e9f6b26dec","target":"graph","created_at":"2026-05-18T02:44:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"The Double Folding Test of Unimodality resolves systematic failures of the original FTU on Dirac and Gaussian mixtures and enhances multimodality detection."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"The folding test of unimodality misclassifies certain multimodal mixtures as unimodal, but a double-folding version corrects the error."}],"snapshot_sha256":"58b34b7ff408821ca71c0326ac39e197170213aabe69447a0eceb82a4ad8bb9b"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Anne M. Ruiz, Aurore Archimbaud, Colombe Becquart, Zaineb Smida","cross_cats":[],"headline":"The folding test of unimodality misclassifies certain multimodal mixtures as unimodal, but a double-folding version corrects the error.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-05-13T10:40:11Z","title":"A Note on the Folding Test of Unimodality: limitation and improved alternative"},"references":{"count":24,"internal_anchors":0,"resolved_work":24,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"The annals of Statistics , pages=","work_id":"4f9c6967-a4d4-49a1-ad5f-cace29b48f52","year":1985},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"Are your data gathered? , abstract =","work_id":"96091fc6-31a5-4b65-809a-e31c8f7356b0","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"New statistical methods for data mining, contributions to anomaly detection and unimodality testing , copyright =","work_id":"edce8f3d-e101-42b5-b45f-025606de6200","year":2019},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"arXiv preprint arXiv:2311.16614 , author =","work_id":"dd9a4913-eb0b-49f1-8cfe-9997244be76f","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"Journal of the Royal Statistical Society Series B: Statistical Methodology , author =","work_id":"b953a2d9-e38e-48c3-80aa-1593d5176451","year":1981}],"snapshot_sha256":"49ba3d212dde7b784587603d9ab17a957ed2d087f9d876d5a2a5802c42e5b4c9"},"source":{"id":"2605.13326","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-14T18:08:03.080870Z","id":"f560fc36-47df-4b91-931d-6a1c3adf9eb3","model_set":{"reader":"grok-4.3"},"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","pith_extraction_headline":"The folding test of unimodality misclassifies certain multimodal mixtures as unimodal, but a double-folding version corrects the error.","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.","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."}},"verdict_id":"f560fc36-47df-4b91-931d-6a1c3adf9eb3"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f6d97c2f514fb355bbc95f337b4fe2f6c2ddf1b1c5049013a2e8eccf5bd475cf","target":"record","created_at":"2026-05-18T02:44:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"370993d3ab16aa30fbad6235be5219e44fccec73cca7568b815f82b43a90edc4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-05-13T10:40:11Z","title_canon_sha256":"272bf61f58f668f1dc5d11c667a13a577ea5447a6ccab46681c3704624c2a075"},"schema_version":"1.0","source":{"id":"2605.13326","kind":"arxiv","version":1}},"canonical_sha256":"80478a42d6126bcc9a586f7315ccba7b7e825b999e1c2ea355339648c5b5e3ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80478a42d6126bcc9a586f7315ccba7b7e825b999e1c2ea355339648c5b5e3ae","first_computed_at":"2026-05-18T02:44:48.616490Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:48.616490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YpFdgCCx8D8/zWVxRGikSvhw6TjFF9BlIhdoYwJ1lu8+hO0I1Vkiih9KwqDapw48E5DPN3+Q9Lr/sJc8h+qDBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:48.616896Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.13326","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6d97c2f514fb355bbc95f337b4fe2f6c2ddf1b1c5049013a2e8eccf5bd475cf","sha256:b4fb9b40ac7bfaf229489a06449a56f28da9eafa4046fb1b7b7fe6e9f6b26dec"],"state_sha256":"770c28de9e0da67ff0a2d415dc8eec9e2eb1ae2cd5a3dce6bbd2419522911640"}