Pith Number

pith:PKC2YZPI

pith:2022:PKC2YZPIHW64EEUGTTQDBAXHE5

not attested not anchored not stored refs pending

Anisotropic Hardy-Sobolev inequality in mixed Lorentz spaces with applications to the axisymmetric Navier-Stokes equations

Huan Yu, Wei Wei, Yanqing Wang, Yike Huang

arxiv:2205.13893 v1 · 2022-05-27 · 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{PKC2YZPIHW64EEUGTTQDBAXHE5}

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	2026-07-05T04:26:53.295050Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a85ac65e83dbdc212869ce03082e7275e716e3c7a5aa8ee0c886eaac688c146

Aliases

arxiv: 2205.13893 · arxiv_version: 2205.13893v1 · doi: 10.48550/arxiv.2205.13893 · pith_short_12: PKC2YZPIHW64 · pith_short_16: PKC2YZPIHW64EEUG · pith_short_8: PKC2YZPI

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/PKC2YZPIHW64EEUGTTQDBAXHE5 \
  | 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: 7a85ac65e83dbdc212869ce03082e7275e716e3c7a5aa8ee0c886eaac688c146

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bce7c7967420deaf227adf14b29e65ee09fa76596fd80147c90930ddf6552ab6",
    "cross_cats_sorted": [
      "math.CA",
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2022-05-27T10:53:03Z",
    "title_canon_sha256": "e423db810b0e3dd81f6ee7c424814565712551479f476428f507d74ded53d69d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2205.13893",
    "kind": "arxiv",
    "version": 1
  }
}