Pith Number

pith:UUUSAIPD

pith:2007:UUUSAIPDV62CPW3I3ZQVY2RBR2

not attested not anchored not stored refs pending

Regularity of Leray-Hopf solutions to Navier-Stokes equations

Jian Zhai

arxiv:0712.3090 v2 · 2007-12-19 · math.AP · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UUUSAIPDV62CPW3I3ZQVY2RBR2}

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	2026-05-18T04:09:04.255700Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a5292021e3afb427db68de615c6a218e8ed5533c3fcf6900b3f7a8c233beee2e

Aliases

arxiv: 0712.3090 · arxiv_version: 0712.3090v2 · doi: 10.48550/arxiv.0712.3090 · pith_short_12: UUUSAIPDV62C · pith_short_16: UUUSAIPDV62CPW3I · pith_short_8: UUUSAIPD

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/UUUSAIPDV62CPW3I3ZQVY2RBR2 \
  | 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: a5292021e3afb427db68de615c6a218e8ed5533c3fcf6900b3f7a8c233beee2e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "85a9d28e64298128bdb4a847cc018cc0edd4f1621cacbdd6859466ffe4bb2569",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2007-12-19T02:16:50Z",
    "title_canon_sha256": "963c443494bd2492da71e01cf4a4ebeacbb1f2d90cf303424d579fea0a93c902"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.3090",
    "kind": "arxiv",
    "version": 2
  }
}