Pith Number

pith:W2KU7HX2

pith:2026:W2KU7HX226ZRO6TJZ2ZA3JW63R

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General Grad-Shafranov Equation

Ye Shen

A single differential-form expression unifies the Grad-Shafranov equation across symmetric force-free plasma configurations.

arxiv:2605.08597 v1 · 2026-05-09 · gr-qc · astro-ph.HE · physics.plasm-ph

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Claims

C1strongest claim

via the language of differential form, we provide a general expression of Grad-Shafranov equation, from which the expression in any specific situation can be quickly obtained. Additionally, we present a Lagrangian density for a scalar field whose on-shell condition is precisely the Grad-Shafranov equation.

C2weakest assumption

That every physically relevant symmetric force-free configuration can be recovered from the single differential-form expression without extra assumptions or coordinate singularities that break the claimed generality.

C3one line summary

A general Grad-Shafranov equation is obtained via differential forms, together with a scalar-field Lagrangian that yields the equation on-shell.

References

74 extracted · 74 resolved · 0 Pith anchors

[1] The rank cannot be exceed the dimen- sion of the manifold (or it is identically zero)

[2] closed” if d F = 0. It is called “exact

[3] It is feasible to deﬁne the metric-compatible volume element via the coordinate basis {ea} as: ǫ := √ |g|e1 ∧

[4] In these cases, it is convenient to decompose the manifold into several submanifolds

[5] (5) Here we prove the second step of Eq

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-02T02:04:18.709764Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b6954f9efad7b3177a69ceb20da6dedc453a38c99264709651666ce6ded0e89b

Aliases

arxiv: 2605.08597 · arxiv_version: 2605.08597v1 · doi: 10.48550/arxiv.2605.08597 · pith_short_12: W2KU7HX226ZR · pith_short_16: W2KU7HX226ZRO6TJ · pith_short_8: W2KU7HX2

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/W2KU7HX226ZRO6TJZ2ZA3JW63R \
  | 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: b6954f9efad7b3177a69ceb20da6dedc453a38c99264709651666ce6ded0e89b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7f1a55a5428ccb492793939cfc673f0ce34bb4b15994eb0fd97e7035ebb0ea12",
    "cross_cats_sorted": [
      "astro-ph.HE",
      "physics.plasm-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-05-09T01:35:35Z",
    "title_canon_sha256": "c51432db4c6a50bf9844a3946fb10679910d9c0ead495d22c36c2b1dfeb82c18"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.08597",
    "kind": "arxiv",
    "version": 1
  }
}