Pith Number

pith:36S3E762

pith:2015:36S3E7625GQZGECKWUJMRMZDHA

not attested not anchored not stored refs pending

Multiplicity of positive solutions for a fractional Laplacian equations involving critical nonlinearity

Hongying Jiao, Jinguo Zhang, Xiaochun Liu

arxiv:1502.02222 v1 · 2015-02-08 · 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{36S3E7625GQZGECKWUJMRMZDHA}

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	2026-05-18T02:27:43.291060Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dfa5b27fdae9a193104ab512c8b32338210af072336a6163fa9a5cb35067555a

Aliases

arxiv: 1502.02222 · arxiv_version: 1502.02222v1 · doi: 10.48550/arxiv.1502.02222 · pith_short_12: 36S3E7625GQZ · pith_short_16: 36S3E7625GQZGECK · pith_short_8: 36S3E762

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/36S3E7625GQZGECKWUJMRMZDHA \
  | 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: dfa5b27fdae9a193104ab512c8b32338210af072336a6163fa9a5cb35067555a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c1c59b1042837c3d33b4b586f56b035c685603acdfdf9656ee8e90a08d45ccbf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-02-08T07:20:32Z",
    "title_canon_sha256": "36ae4b4a44c811231397c5cf1cf120b6cadf8af822c67f408f881feb2f277210"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.02222",
    "kind": "arxiv",
    "version": 1
  }
}