Pith Number

pith:JO24HYI3

pith:2026:JO24HYI35GPA2TK24KGL5AEAQW

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Evaluating the skill of a geometric early warning for tipping in a rapidly forced nonlinear system

Paul D. L. Ritchie, Peter Ashwin, Sneha Kachhara

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.

arxiv:2605.16128 v1 · 2026-05-15 · math.DS

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\pithnumber{JO24HYI35GPA2TK24KGL5AEAQW}

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We show that the skill of the geometric early warning compares favourably with simple thresholds.

C2weakest 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.

C3one 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.

References

41 extracted · 41 resolved · 0 Pith anchors

[1] Jackson, Courtney Quinn, and Richard A 2019

[2] Rate-induced tipping from periodic attractors: Partial tipping and connecting orbits.Chaos: An Interdisciplinary Journal of Nonlinear Science, 28(3), 2018 2018

[3] von der Heydt, and Paul D.L 2025

[4] 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): 2021

[5] Contrasting chaotic and stochastic forcing: Tipping windows and attractor crises.SIAM Journal on Applied Dynamical Systems, 24(1):277–316, 2025 2025

Receipt and verification

First computed	2026-05-20T00:01:54.024809Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4bb5c3e11be99e0d4d5ae28cbe808085be189444b8bf0bb22f705f3a6a5c2910

Aliases

arxiv: 2605.16128 · arxiv_version: 2605.16128v1 · doi: 10.48550/arxiv.2605.16128 · pith_short_12: JO24HYI35GPA · pith_short_16: JO24HYI35GPA2TK2 · pith_short_8: JO24HYI3

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JO24HYI35GPA2TK24KGL5AEAQW \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 4bb5c3e11be99e0d4d5ae28cbe808085be189444b8bf0bb22f705f3a6a5c2910

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cfe8f608256cec5e96043cad5f321f849ec13a267eef24cb4d1445080b4c226c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-05-15T16:13:47Z",
    "title_canon_sha256": "05e8f87c12924b55d608656e958b4a22dc642543f62fddfa60c25be4069f5bb4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16128",
    "kind": "arxiv",
    "version": 1
  }
}