Pith Number

pith:X4QOBA2M

pith:2013:X4QOBA2MRNGMSCAAAJSHYIE4U4

not attested not anchored not stored refs pending

On whether zero is in the global attractor of the 2D Navier-Stokes equations

Bingsheng Zhang, Ciprian Foias, Michael Jolly, Yong Yang

arxiv:1312.6716 v1 · 2013-12-23 · 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{X4QOBA2MRNGMSCAAAJSHYIE4U4}

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	2026-05-18T01:45:42.234710Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf20e0834c8b4cc9080002647c209ca70d38c16050d718144fab47946467ea9b

Aliases

arxiv: 1312.6716 · arxiv_version: 1312.6716v1 · doi: 10.48550/arxiv.1312.6716 · pith_short_12: X4QOBA2MRNGM · pith_short_16: X4QOBA2MRNGMSCAA · pith_short_8: X4QOBA2M

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/X4QOBA2MRNGMSCAAAJSHYIE4U4 \
  | 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: bf20e0834c8b4cc9080002647c209ca70d38c16050d718144fab47946467ea9b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "933e0d81c2782ee2f60cde8d9ffb3410f5f02e4821b107439537c8f23e4194e1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-12-23T22:38:29Z",
    "title_canon_sha256": "ff265609c85cf55dda1654a0d82bb8fd8f60c4b4f0a018c1151d4c19edb4749b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.6716",
    "kind": "arxiv",
    "version": 1
  }
}