Pith Number

pith:WDVPACLP

pith:2010:WDVPACLPMXREULKXXBPIJLS2CE

not attested not anchored not stored refs pending

N-Laplacian equations in $\mathbb{R}^{N}$ with subcritical and critical growth without the Ambrosetti-Rabinowitz condition

Guozhen Lu, Nhuyen Lam

arxiv:1012.5489 v1 · 2010-12-25 · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WDVPACLPMXREULKXXBPIJLS2CE}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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.

Receipt and verification

First computed	2026-05-18T04:32:23.271190Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0eaf0096f65e24a2d57b85e84ae5a113cad4da36be048928c8b6726d7b5084e

Aliases

arxiv: 1012.5489 · arxiv_version: 1012.5489v1 · doi: 10.48550/arxiv.1012.5489 · pith_short_12: WDVPACLPMXRE · pith_short_16: WDVPACLPMXREULKX · pith_short_8: WDVPACLP

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/WDVPACLPMXREULKXXBPIJLS2CE \
  | 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: b0eaf0096f65e24a2d57b85e84ae5a113cad4da36be048928c8b6726d7b5084e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e5e178837f042c2976046ee4f80758066c43faa06838ce4f7a4af3fdad72aba1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-12-25T18:30:41Z",
    "title_canon_sha256": "0249830e3d2955e7eddcae585dc4f999e4bf0e510b987c79c85c330026f533c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.5489",
    "kind": "arxiv",
    "version": 1
  }
}