Pith Number

pith:RRR7XEJ4

pith:2011:RRR7XEJ4QYVKHMGRZ7GML3OMI4

not attested not anchored not stored refs pending

A Nonlinear Elliptic PDE with Two Sobolev-Hardy Critical Exponents

Chang-shou Lin, Yanyan Li

arxiv:1102.4134 v1 · 2011-02-21 · 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{RRR7XEJ4QYVKHMGRZ7GML3OMI4}

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	2026-05-18T02:03:07.305179Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8c63fb913c862aa3b0d1cfccc5edcc4714d862f041a9efa2b0374ee16bca112d

Aliases

arxiv: 1102.4134 · arxiv_version: 1102.4134v1 · doi: 10.48550/arxiv.1102.4134 · pith_short_12: RRR7XEJ4QYVK · pith_short_16: RRR7XEJ4QYVKHMGR · pith_short_8: RRR7XEJ4

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/RRR7XEJ4QYVKHMGRZ7GML3OMI4 \
  | 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: 8c63fb913c862aa3b0d1cfccc5edcc4714d862f041a9efa2b0374ee16bca112d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "390e0a64a6bbd6f3fff077b24fbe93b29398a4e8c214fd5c89d1d807434a6447",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-02-21T05:14:19Z",
    "title_canon_sha256": "d4176779eeb4199067da92b8efc6a5dbfdd2b1c389f545f5b94e385f883da03f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.4134",
    "kind": "arxiv",
    "version": 1
  }
}