Pith Number

pith:5PPTZ7MP

pith:2023:5PPTZ7MPHVPIWMZPO4A6N6IZQL

not attested not anchored not stored refs pending

Classification of solutions to the anisotropic $N$-Liouville equation in $\mathbb{R}^N$

Giulio Ciraolo, Xiaoliang Li

arxiv:2306.12039 v2 · 2023-06-21 · math.AP

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5PPTZ7MPHVPIWMZPO4A6N6IZQL}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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.

Cited by

1 paper in Pith

Brezis-Nirenberg-type results for the anisotropic $p$-Laplacian

Receipt and verification

First computed	2026-07-05T08:23:10.085156Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebdf3cfd8f3d5e8b332f7701e6f91982f4c7787b612cfde2efecc7da11bd0378

Aliases

arxiv: 2306.12039 · arxiv_version: 2306.12039v2 · doi: 10.48550/arxiv.2306.12039 · pith_short_12: 5PPTZ7MPHVPI · pith_short_16: 5PPTZ7MPHVPIWMZP · pith_short_8: 5PPTZ7MP

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5PPTZ7MPHVPIWMZPO4A6N6IZQL \
  | 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: ebdf3cfd8f3d5e8b332f7701e6f91982f4c7787b612cfde2efecc7da11bd0378

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f8df2da1f32bd51bfb080b2a0785800ab175747b8b7be34cc8335ec4d53b574",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2023-06-21T06:08:47Z",
    "title_canon_sha256": "06e0fd2c675003ca3cc46a4e32789111dc0741025c0111a44114f34f23e9dbc6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2306.12039",
    "kind": "arxiv",
    "version": 2
  }
}