Pith Number

pith:4JOJSPTU

pith:2014:4JOJSPTUIPHIMCCL4MUTFF2NDR

not attested not anchored not stored refs pending

Blow-up criterion for the compressible magnetohydrodynamic equations with vacuum

Shengguo Zhu

arxiv:1402.0542 v2 · 2014-02-03 · 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{4JOJSPTUIPHIMCCL4MUTFF2NDR}

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	2026-05-18T02:41:01.741975Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e25c993e7443ce86084be32932974d1c689cd2abc252a87b91641decaa6f65ee

Aliases

arxiv: 1402.0542 · arxiv_version: 1402.0542v2 · doi: 10.48550/arxiv.1402.0542 · pith_short_12: 4JOJSPTUIPHI · pith_short_16: 4JOJSPTUIPHIMCCL · pith_short_8: 4JOJSPTU

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/4JOJSPTUIPHIMCCL4MUTFF2NDR \
  | 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: e25c993e7443ce86084be32932974d1c689cd2abc252a87b91641decaa6f65ee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5e3b928f678b77c300088568177a337315cdcbd21a29c5b395b9272fb48fb27",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2014-02-03T23:02:04Z",
    "title_canon_sha256": "98e3ee22aa8d45a63c26545eba9d5f9a8d7aacb93a371474444cf9063f71238c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1402.0542",
    "kind": "arxiv",
    "version": 2
  }
}