Pith Number

pith:IN2F7PNV

pith:2022:IN2F7PNVBAQ7NEY7B4SQH24ZLA

not attested not anchored not stored refs pending

Gagliardo-Nirenberg inequality in anisotropic Lebesgue spaces and energy equality in the Navier-Stokes equations

Wei Wei, Xue Mei, Yanqing Wang

arxiv:2204.07479 v1 · 2022-04-15 · math.AP · math.CA · math.FA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IN2F7PNVBAQ7NEY7B4SQH24ZLA}

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	2026-07-05T04:15:04.560573Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

43745fbdb50821f6931f0f2503eb99582f1e1510b509d3644ac66e34a9fcda51

Aliases

arxiv: 2204.07479 · arxiv_version: 2204.07479v1 · doi: 10.48550/arxiv.2204.07479 · pith_short_12: IN2F7PNVBAQ7 · pith_short_16: IN2F7PNVBAQ7NEY7 · pith_short_8: IN2F7PNV

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/IN2F7PNVBAQ7NEY7B4SQH24ZLA \
  | 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: 43745fbdb50821f6931f0f2503eb99582f1e1510b509d3644ac66e34a9fcda51

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "541fab58866002196144876aba259e0d21795a61d8586cf59333c7dbe6cf8e61",
    "cross_cats_sorted": [
      "math.CA",
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2022-04-15T14:28:56Z",
    "title_canon_sha256": "cd22109245d2b504c34e472339d4dcf58a581050622bd7b234dd71a39af9d70b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2204.07479",
    "kind": "arxiv",
    "version": 1
  }
}