Pith Number

pith:KO2ZEGV4

pith:2010:KO2ZEGV4MPODH7P2CQSRVUWAUH

not attested not anchored not stored refs pending

Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor

Chongsheng Cao, Edriss S. Titi

arxiv:1005.4463 v1 · 2010-05-25 · 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{KO2ZEGV4MPODH7P2CQSRVUWAUH}

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	2026-05-18T02:07:14.899998Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53b5921abc63dc33fdfa14251ad2c0a1f850ee84064e66ca685f681b912a6cf0

Aliases

arxiv: 1005.4463 · arxiv_version: 1005.4463v1 · doi: 10.48550/arxiv.1005.4463 · pith_short_12: KO2ZEGV4MPOD · pith_short_16: KO2ZEGV4MPODH7P2 · pith_short_8: KO2ZEGV4

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/KO2ZEGV4MPODH7P2CQSRVUWAUH \
  | 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: 53b5921abc63dc33fdfa14251ad2c0a1f850ee84064e66ca685f681b912a6cf0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6cf0a43cc99e73e0e312c664ddc444c6c4b3b7610a6f68a9310606b533ac0059",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-05-25T00:57:52Z",
    "title_canon_sha256": "866f0ab242d37478d3ab1cbcce76b5588ce2e93608f07e2b0804a7056a4d5474"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.4463",
    "kind": "arxiv",
    "version": 1
  }
}