Pith Number

pith:FDWCKBCY

pith:2010:FDWCKBCYJJ3YCOYVYBRA6S6XFH

not attested not anchored not stored refs pending

A Liouville Theorem for the Axially-symmetric Navier-Stokes Equations

Qi S. Zhang, Zhen Lei

arxiv:1011.5066 v2 · 2010-11-23 · 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{FDWCKBCYJJ3YCOYVYBRA6S6XFH}

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	2026-05-18T04:34:37.981547Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

28ec2504584a77813b15c0620f4bd729fe39869b7186a282d799df84ef55edf3

Aliases

arxiv: 1011.5066 · arxiv_version: 1011.5066v2 · doi: 10.48550/arxiv.1011.5066 · pith_short_12: FDWCKBCYJJ3Y · pith_short_16: FDWCKBCYJJ3YCOYV · pith_short_8: FDWCKBCY

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/FDWCKBCYJJ3YCOYVYBRA6S6XFH \
  | 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: 28ec2504584a77813b15c0620f4bd729fe39869b7186a282d799df84ef55edf3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "54e4110da71193f6e717dd0146247602d260b0725bdf0be04ebf2cff1e9eadc0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-11-23T11:38:15Z",
    "title_canon_sha256": "a6b32f43f4d31659f3d6a3853aad46e2363a1641f11b17ef668774463f357bac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.5066",
    "kind": "arxiv",
    "version": 2
  }
}