Pith Number

pith:JBICUOBP

pith:2025:JBICUOBPDN3MWIO5WPKRJV4YTJ

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On the super-Liouville equations on the sphere

Chunqin Zhou, Mingyang Han

A new natural constraint set allows variational methods to prove existence of least-energy solutions to the super-Liouville equation on the sphere when coefficients are even.

arxiv:2509.16712 v5 · 2025-09-20 · math.AP · math-ph · math.FA · math.MP

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Claims

C1strongest claim

By introducing a new natural constraint A, and employing variational methods, we establish the existence of a least-energy solution when the coefficient functions are even. Furthermore, we obtain that the solution is nontrivial, i.e., ψ ≢ 0, whenever λ1(h2, h1) < 1.

C2weakest assumption

The coefficient functions are even; this symmetry is invoked to guarantee that the variational minimization on the new constraint set A produces a critical point satisfying the equation.

C3one line summary

Proves compactness of solutions in low-energy and Möbius-invariant regimes and existence of least-energy nontrivial solutions to the super-Liouville equation on the sphere for even positive coefficients.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-19T16:12:48.018294Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

48502a382f1b76cb21ddb3d514d7989a76f0c01246131fbff2487fad7483d72c

Aliases

arxiv: 2509.16712 · arxiv_version: 2509.16712v5 · doi: 10.48550/arxiv.2509.16712 · pith_short_12: JBICUOBPDN3M · pith_short_16: JBICUOBPDN3MWIO5 · pith_short_8: JBICUOBP

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JBICUOBPDN3MWIO5WPKRJV4YTJ \
  | 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: 48502a382f1b76cb21ddb3d514d7989a76f0c01246131fbff2487fad7483d72c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3ff4920247fff31a308af2eeeb484482e9557e869a82a952951233471a59292f",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-09-20T14:49:49Z",
    "title_canon_sha256": "ef9d073f544792652aaca6ced247e570bf20f9ced0ec15e76d25a127f7803ff9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.16712",
    "kind": "arxiv",
    "version": 5
  }
}