Pith Number

pith:RHTH2AXG

pith:2026:RHTH2AXGPRHV74YPCBHZ23D2EJ

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FEG-Pro: Forecast-Error Growth Profiling for Finite-Horizon Instability Analysis of Nonlinear Time Series

Andrei Velichko, Bruno Carpentieri, Mudassir Shams, N'Gbo N'Gbo

A forecast-error growth slope from scalar time series estimates the largest Lyapunov exponent when the growth curve shows a quasi-linear regime.

arxiv:2605.17282 v1 · 2026-05-17 · nlin.CD · cs.LG · math.DS

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Claims

C1strongest claim

When the error-growth curve supports a quasi-linear regime, the finite-horizon forecast-error growth slope lambda_FEG can be compared with reference largest Lyapunov exponents as an estimate of the dominant instability rate.

C2weakest assumption

The forecasting procedure (autocorrelation-guided sparse histories plus distance-weighted k-nearest-neighbor multi-horizon prediction) accurately captures the local expansion rates of the underlying dynamics so that the resulting error-growth slope approximates the largest Lyapunov exponent in quasi-linear regimes.

C3one line summary

FEG-Pro estimates finite-horizon forecast-error growth slopes from scalar time series via kNN multi-horizon forecasting as proxies for largest Lyapunov exponents, while extracting additional profile descriptors.

References

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[1] Takens, Detecting strange attractors in turbulence, Lecture Notes in Mathematics 898 (1981) 366–381 1981

[2] A. Wolf, J. B. Swift, H. L. Swinney, J. A. Vastano, Determining lyapunov exponents from a time series, Physica D: Nonlinear Phenomena 16 (3) (1985) 285–317. 28 1985

[3] M. T. Rosenstein, J. J. Collins, C. J. De Luca, A practical method for calculating largest lyapunov exponents from small data sets, Physica D: Nonlinear Phenomena 65 (1–2) (1993) 117–134 1993

[4] Kantz, A robust method to estimate the maximal lyapunov exponent of a time series, Physics Letters A 185 (1) (1994) 77–87 1994

[5] H. D. I. Abarbanel, Analysis of Observed Chaotic Data, Springer, 1996 1996

Formal links

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Receipt and verification

First computed	2026-05-20T00:03:49.641269Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

89e67d02e67c4f5ff30f104f9d6c7a2245bfd88b4e6b329aa3be0e361f1f9998

Aliases

arxiv: 2605.17282 · arxiv_version: 2605.17282v1 · doi: 10.48550/arxiv.2605.17282 · pith_short_12: RHTH2AXGPRHV · pith_short_16: RHTH2AXGPRHV74YP · pith_short_8: RHTH2AXG

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/RHTH2AXGPRHV74YPCBHZ23D2EJ \
  | 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: 89e67d02e67c4f5ff30f104f9d6c7a2245bfd88b4e6b329aa3be0e361f1f9998

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e295aa1651e9d6ed504b9fe7446e0687312cc478942f788850bdd529384bd93",
    "cross_cats_sorted": [
      "cs.LG",
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "nlin.CD",
    "submitted_at": "2026-05-17T06:38:37Z",
    "title_canon_sha256": "568e31487a2bf5b4b4894bb6cbc122b8aac1d4c57ad6da60c4414a2f4d738135"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17282",
    "kind": "arxiv",
    "version": 1
  }
}