Pith Number

pith:JZWOZHL6

pith:2015:JZWOZHL6YKTW4JNTDMEMQDU4AU

not attested not anchored not stored refs pending

Blow-up of critical norms for the 3-D Navier-Stokes equations

Wendong Wang, Zhifei Zhang

arxiv:1510.02589 v1 · 2015-10-09 · 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{JZWOZHL6YKTW4JNTDMEMQDU4AU}

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	2026-05-18T01:30:41.989712Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4e6cec9d7ec2a76e25b31b08c80e9c052e3e8c0a82f03621edd43be48ff8cdac

Aliases

arxiv: 1510.02589 · arxiv_version: 1510.02589v1 · doi: 10.48550/arxiv.1510.02589 · pith_short_12: JZWOZHL6YKTW · pith_short_16: JZWOZHL6YKTW4JNT · pith_short_8: JZWOZHL6

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/JZWOZHL6YKTW4JNTDMEMQDU4AU \
  | 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: 4e6cec9d7ec2a76e25b31b08c80e9c052e3e8c0a82f03621edd43be48ff8cdac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be267776bb187f54035822fb3c758ac17c41acb0dac330d2081fe2d5ffce6ee4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-10-09T08:28:01Z",
    "title_canon_sha256": "4df5ebcebc4221348f6b4340598d367b073aabf91c8a7702e14d6d18246a4ac9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.02589",
    "kind": "arxiv",
    "version": 1
  }
}