Pith Number

pith:435WH35Y

pith:2015:435WH35YAUK573VGU3ZVAJS34X

not attested not anchored not stored refs pending

A nonlinear elliptic PDE with multiple Hardy-Sobolev critical exponents in $\mathbb{R}^N$

Wenming Zou, Xuexiu Zhong

arxiv:1504.01133 v2 · 2015-04-05 · 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{435WH35YAUK573VGU3ZVAJS34X}

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	2026-05-18T00:27:10.259741Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6fb63efb80515dfeea6a6f350265be5f51fa44e480ff00bb5a44292059cc2d7

Aliases

arxiv: 1504.01133 · arxiv_version: 1504.01133v2 · doi: 10.48550/arxiv.1504.01133 · pith_short_12: 435WH35YAUK5 · pith_short_16: 435WH35YAUK573VG · pith_short_8: 435WH35Y

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/435WH35YAUK573VGU3ZVAJS34X \
  | 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: e6fb63efb80515dfeea6a6f350265be5f51fa44e480ff00bb5a44292059cc2d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d27022c862c66207fcfbf361d8ed2cb972932e3ef37623110b250b9b44f4405",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-04-05T16:02:15Z",
    "title_canon_sha256": "a339d9a40fdac62d4f1f3cf106059eea13d23e4193efd6ad392796cd61009a08"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.01133",
    "kind": "arxiv",
    "version": 2
  }
}