{"paper":{"title":"Evaluating the skill of a geometric early warning for tipping in a rapidly forced nonlinear system","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A geometric early warning based on signed distance to an approximate R-tipping threshold predicts future states in rapidly forced systems better than simple thresholds.","cross_cats":[],"primary_cat":"math.DS","authors_text":"Paul D. L. Ritchie, Peter Ashwin, Sneha Kachhara","submitted_at":"2026-05-15T16:13:47Z","abstract_excerpt":"The future behavioural fate of a forced nonlinear system can depend sensitively on the forcing profile as well as natural fluctuations within the system. This is especially the case for rate-induced tipping, where the forcing pushes the system to a basin boundary of a future behaviour and small changes in the forcing can lead to drastically different eventual behaviours. This sensitivity may be present only for a limited period of time, for example when the forcing is most rapidly changing. Moreover, critical slowing down based methods fail to be informative in such cases. We investigate a geo"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that the skill of the geometric early warning compares favourably with simple thresholds.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That an approximate R-tipping threshold, constructed from the system dynamics and the specified future forcing profile, can be computed with sufficient accuracy to serve as a reliable early-warning distance without requiring exhaustive sampling of natural fluctuations.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The geometric R-tipping indicator shows superior skill to simple thresholds for early prediction of tipping under rapid forcing in a 3-box AMOC model.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A geometric early warning based on signed distance to an approximate R-tipping threshold predicts future states in rapidly forced systems better than simple thresholds.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"8f9e989cd27e53f9254f69c0dbe75068b23c6c7b07fe877e789b8da168ce54ea"},"source":{"id":"2605.16128","kind":"arxiv","version":1},"verdict":{"id":"f0856b54-2b0d-4f40-af38-2a0bdb7f02f8","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T18:40:43.133003Z","strongest_claim":"We show that the skill of the geometric early warning compares favourably with simple thresholds.","one_line_summary":"The geometric R-tipping indicator shows superior skill to simple thresholds for early prediction of tipping under rapid forcing in a 3-box AMOC model.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That an approximate R-tipping threshold, constructed from the system dynamics and the specified future forcing profile, can be computed with sufficient accuracy to serve as a reliable early-warning distance without requiring exhaustive sampling of natural fluctuations.","pith_extraction_headline":"A geometric early warning based on signed distance to an approximate R-tipping threshold predicts future states in rapidly forced systems better than simple thresholds."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16128/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T19:01:18.955319Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T18:51:36.039425Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:33.379381Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T16:41:55.467490Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"f3f0c5043f130f88ec004bcca5e9ad723faa434676406cf8bab8289dfc31b587"},"references":{"count":41,"sample":[{"doi":"","year":2019,"title":"Jackson, Courtney Quinn, and Richard A","work_id":"0dc6e6fc-6df6-44be-ac42-b2cd783d8f53","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2018,"title":"Rate-induced tipping from periodic attractors: Partial tipping and connecting orbits.Chaos: An Interdisciplinary Journal of Nonlinear Science, 28(3), 2018","work_id":"c8dd94d6-37dc-4079-83eb-2d0644d9f099","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"von der Heydt, and Paul D.L","work_id":"0b4f7c01-1b46-4c83-88ba-11c8a6f612b0","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2021,"title":"Peter Ashwin and Julian Newman. Physical invariant measures and tipping probabilities for chaotic attractors of asymptotically autonomous systems.The European Physical Journal Special Topics, 230(16):","work_id":"a4ad8afc-6ab0-44d0-9aaa-74201f470491","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Contrasting chaotic and stochastic forcing: Tipping windows and attractor crises.SIAM Journal on Applied Dynamical Systems, 24(1):277–316, 2025","work_id":"38fc7e9c-c69c-464c-aa0f-f032b767c169","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":41,"snapshot_sha256":"ca8583ea2aaf7163b856d895c467f8da6d5e0081127cc428ff2bd8371a463ea5","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"}