Pith Number

pith:VSXNH4PL

pith:2017:VSXNH4PLG5IPASAVEFNEEXJHW7

not attested not anchored not stored refs pending

Improved Liouville theorems for axially symmetric Navier-Stokes equations

Na Zhao, Qi S Zhang, Zhen Lei

arxiv:1701.00868 v1 · 2017-01-03 · 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{VSXNH4PLG5IPASAVEFNEEXJHW7}

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	2026-05-18T00:53:22.021137Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

acaed3f1eb3750f04815215a425d27b7e1139577eebe9c50db62ebb495437a3c

Aliases

arxiv: 1701.00868 · arxiv_version: 1701.00868v1 · doi: 10.48550/arxiv.1701.00868 · pith_short_12: VSXNH4PLG5IP · pith_short_16: VSXNH4PLG5IPASAV · pith_short_8: VSXNH4PL

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/VSXNH4PLG5IPASAVEFNEEXJHW7 \
  | 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: acaed3f1eb3750f04815215a425d27b7e1139577eebe9c50db62ebb495437a3c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4a8aacb5c1759cbed654b93b0cf3fa41990a649419d3d883bdb4c8bdc8373e14",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-01-03T23:38:09Z",
    "title_canon_sha256": "47f0c3ccbf7381606fe9563fcc47a499235b24aaa5100b450e2bb9d1d4c51ef3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1701.00868",
    "kind": "arxiv",
    "version": 1
  }
}