Pith Number

pith:5WY3JBZZ

pith:2014:5WY3JBZZWTC3O75WQ5CGHR467F

not attested not anchored not stored refs pending

Infinitely many non-radial sign-changing solutions for a Fractional Laplacian equation with critical nonlinearity

Fei Fang

arxiv:1408.3187 v1 · 2014-08-14 · 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{5WY3JBZZWTC3O75WQ5CGHR467F}

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	2026-05-18T02:45:13.601453Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

edb1b48739b4c5b77fb6874463c79ef97372f9e598d0191e5be91855ca2d6b08

Aliases

arxiv: 1408.3187 · arxiv_version: 1408.3187v1 · doi: 10.48550/arxiv.1408.3187 · pith_short_12: 5WY3JBZZWTC3 · pith_short_16: 5WY3JBZZWTC3O75W · pith_short_8: 5WY3JBZZ

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/5WY3JBZZWTC3O75WQ5CGHR467F \
  | 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: edb1b48739b4c5b77fb6874463c79ef97372f9e598d0191e5be91855ca2d6b08

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bdb86262e24f00a693e60b8c584699801aad04ae4a9be601564f529bcadb9b0b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2014-08-14T03:24:36Z",
    "title_canon_sha256": "7d0f6875090fe0c89d78d9a82137727db08069038d63c80149bc21536d7f0938"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1408.3187",
    "kind": "arxiv",
    "version": 1
  }
}