Pith Number

pith:E3JFVNKI

pith:2011:E3JFVNKIMVVMILH3W2UKT4MIVF

not attested not anchored not stored refs pending

Blow-up criterions of strong solutions to 3D compressible Navier-Stokes equations with vacuum

Changjiang Zhu, Huanyao Wen

arxiv:1111.2657 v2 · 2011-11-11 · 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{E3JFVNKIMVVMILH3W2UKT4MIVF}

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	2026-05-18T02:52:42.429300Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

26d25ab548656ac42cfbb6a8a9f188a97fcc4bb0b6bc8d7b76887439f122b7d6

Aliases

arxiv: 1111.2657 · arxiv_version: 1111.2657v2 · doi: 10.48550/arxiv.1111.2657 · pith_short_12: E3JFVNKIMVVM · pith_short_16: E3JFVNKIMVVMILH3 · pith_short_8: E3JFVNKI

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/E3JFVNKIMVVMILH3W2UKT4MIVF \
  | 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: 26d25ab548656ac42cfbb6a8a9f188a97fcc4bb0b6bc8d7b76887439f122b7d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a9bf3de7030b18582905136733eb20470984685470a16a6c222e59d0c9147e7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-11-11T04:07:35Z",
    "title_canon_sha256": "01d880029ec115850628101568e9a0807b8f8fe1fb362862028433d08d879a31"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.2657",
    "kind": "arxiv",
    "version": 2
  }
}