Pith Number

pith:QHPXPKXN

pith:2018:QHPXPKXNA6MUHBJFKKLKEFCVXB

not attested not anchored not stored refs pending

Liouville type theorem for critical order Lane-Emden-Hardy equations in $\mathbb{R}^n$

Guolin Qin, Wei Dai, Wenxiong Chen

arxiv:1808.01581 v1 · 2018-08-05 · 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{QHPXPKXNA6MUHBJFKKLKEFCVXB}

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	2026-05-18T00:08:52.536576Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

81df77aaed07994385255296a21455b87396483b8ffe77463bbe0892fa09a256

Aliases

arxiv: 1808.01581 · arxiv_version: 1808.01581v1 · doi: 10.48550/arxiv.1808.01581 · pith_short_12: QHPXPKXNA6MU · pith_short_16: QHPXPKXNA6MUHBJF · pith_short_8: QHPXPKXN

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/QHPXPKXNA6MUHBJFKKLKEFCVXB \
  | 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: 81df77aaed07994385255296a21455b87396483b8ffe77463bbe0892fa09a256

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "853054ad3c5e7b1c2d0068e458f5ec0abec57f07822570381c789472f62a7933",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-08-05T08:38:42Z",
    "title_canon_sha256": "5f6a968661ea4d3547c00b8672d797f8e0b7b7c337c0c0c965ed2da98de7fffa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.01581",
    "kind": "arxiv",
    "version": 1
  }
}