Pith Number

pith:ZKZF7QRS

pith:2026:ZKZF7QRSKSY7WM3FFHWMKABPIX

not attested not anchored not stored refs pending

Solutions of the 3D inhomogeneous incompressible Navier-Stokes system with initial velocity in $VMO^{-1}$

Dongyi Wei, Feng Shao, Ping Zhang, Quoc-Hung Nguyen, Ruilin Hu, Zhifei Zhang

arxiv:2606.20207 v1 · 2026-06-18 · 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{ZKZF7QRSKSY7WM3FFHWMKABPIX}

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	2026-06-19T16:13:05.698752Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cab25fc23254b1fb336529ecc5002f45dd27cd9955644072011a5f24fe283eda

Aliases

arxiv: 2606.20207 · arxiv_version: 2606.20207v1 · doi: 10.48550/arxiv.2606.20207 · pith_short_12: ZKZF7QRSKSY7 · pith_short_16: ZKZF7QRSKSY7WM3F · pith_short_8: ZKZF7QRS

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/ZKZF7QRSKSY7WM3FFHWMKABPIX \
  | 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: cab25fc23254b1fb336529ecc5002f45dd27cd9955644072011a5f24fe283eda

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1affdedac4d8db81b24cab826648250e7d671ae659c71cbb40a04ffc39d2edd2",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-18T13:19:55Z",
    "title_canon_sha256": "62355ca35b27c95afa1f073c81fa86abe3d00ba29a3e8da297752b64aad3b02d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.20207",
    "kind": "arxiv",
    "version": 1
  }
}