Pith Number

pith:JYJKTQM4

pith:2026:JYJKTQM4XDWEMOLQGXZYKYLZWD

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Calculating Domain of Attraction Boundary of Power Systems Based on the Gentlest Ascent Dynamics

Aiqing Zhu, Chenmin Zhang, Jianxi Lin, Sixu Wu, Yang Liu, Yifa Tang

The domain of attraction boundary in power systems equals the closure of the union of stable manifolds of index-1 critical elements.

arxiv:2605.04197 v2 · 2026-05-05 · math.DS · cs.NA · math.NA

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Record completeness

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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

Theoretically, under certain assumptions we prove that the DOA boundary is the closure of the union of stable manifolds of index-1 critical elements, and establish a stability theory for a perturbed GAD system.

C2weakest assumption

The unspecified 'certain assumptions' required for the proof that the DOA boundary equals the closure of the union of stable manifolds of index-1 critical elements; these assumptions are invoked in the theoretical results but not detailed in the abstract.

C3one line summary

The domain of attraction boundary for stable power system equilibria is the closure of the union of stable manifolds of index-1 critical elements, computed via gentlest ascent dynamics, adjoint methods for periodic orbits, and stable manifold algorithms.

Formal links

3 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:05:46.011534Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4e12a9c19cb8ec46397035f3856179b0f21bc1b8c765ab6b3aacd58409d0dbd5

Aliases

arxiv: 2605.04197 · arxiv_version: 2605.04197v2 · doi: 10.48550/arxiv.2605.04197 · pith_short_12: JYJKTQM4XDWE · pith_short_16: JYJKTQM4XDWEMOLQ · pith_short_8: JYJKTQM4

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JYJKTQM4XDWEMOLQGXZYKYLZWD \
  | 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: 4e12a9c19cb8ec46397035f3856179b0f21bc1b8c765ab6b3aacd58409d0dbd5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "389fc9299a13287a0793c0d9ebca74677a4ecdd2052a75757f056f4d20be2f9f",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-05-05T18:40:38Z",
    "title_canon_sha256": "16bd9331359dc610755c07d4f24e95fa7aec15f11434555882b80755aee43ea9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.04197",
    "kind": "arxiv",
    "version": 2
  }
}