Pith Number

pith:P5562ZWL

pith:2010:P5562ZWLLDOOYS5EOJDVPDPCYY

not attested not anchored not stored refs pending

Sufficient and Necessary Conditions for the fractional Gagliardo-Nirenberg Inequalities and applications to Navier-Stokes and generalized boson equations

Baoxiang Wang, Hichem Hajaiej, Luc Molinet, Tohru Ozawa

arxiv:1004.4287 v3 · 2010-04-24 · math.FA · 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{P5562ZWLLDOOYS5EOJDVPDPCYY}

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	2026-05-18T04:30:48.522682Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f7bed66cb58dcec4ba47247578de2c6044a65e29c71bf7b80abf511259ea194

Aliases

arxiv: 1004.4287 · arxiv_version: 1004.4287v3 · doi: 10.48550/arxiv.1004.4287 · pith_short_12: P5562ZWLLDOO · pith_short_16: P5562ZWLLDOOYS5E · pith_short_8: P5562ZWL

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/P5562ZWLLDOOYS5EOJDVPDPCYY \
  | 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: 7f7bed66cb58dcec4ba47247578de2c6044a65e29c71bf7b80abf511259ea194

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1412c2c15c2101e87c2aa6b494210d6743a22f7b4cd5677abd5ce236b585e6cf",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2010-04-24T15:25:32Z",
    "title_canon_sha256": "54faf5439940b60cfa6ca04ea026623e4e349817626c20e2719b3e9eb4aa5a89"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.4287",
    "kind": "arxiv",
    "version": 3
  }
}