Pith Number

pith:JD4WKUZK

pith:2010:JD4WKUZKY64JYAJXSSSCYT5KLK

not attested not anchored not stored refs pending

Structure of Singularities of 3D Axi-symmetric Navier-Stokes Equations

Qi S. Zhang, Zhen Lei

arxiv:1008.4172 v1 · 2010-08-24 · math.AP · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JD4WKUZKY64JYAJXSSSCYT5KLK}

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	2026-05-18T04:41:53.551608Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

48f965532ac7b89c013794a42c4faa5a9d973ad41fad4b605d2706567cc39068

Aliases

arxiv: 1008.4172 · arxiv_version: 1008.4172v1 · doi: 10.48550/arxiv.1008.4172 · pith_short_12: JD4WKUZKY64J · pith_short_16: JD4WKUZKY64JYAJX · pith_short_8: JD4WKUZK

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/JD4WKUZKY64JYAJXSSSCYT5KLK \
  | 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: 48f965532ac7b89c013794a42c4faa5a9d973ad41fad4b605d2706567cc39068

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0bff1c8d9fe9a299786fae7537635f3e2a5e752900cc775143094e86a202766a",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-08-24T22:44:33Z",
    "title_canon_sha256": "77ffec35d9132663d3377f094b936e973a416321c07bc285e290ed2caa0b7ed8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.4172",
    "kind": "arxiv",
    "version": 1
  }
}