Pith Number

pith:LIU2PE33

pith:2016:LIU2PE33XUWNBGEK4GQA3I4QSM

not attested not anchored not stored refs pending

A blow-up criterion for strong solutions to three-dimensional compressible magnetohydrodynamic equations

Xin Zhong

arxiv:1603.08516 v2 · 2016-03-28 · 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{LIU2PE33XUWNBGEK4GQA3I4QSM}

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	2026-05-18T01:17:58.958192Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5a29a7937bbd2cd0988ae1a00da390932c2cdec96732054d8089ce09a8e72dd3

Aliases

arxiv: 1603.08516 · arxiv_version: 1603.08516v2 · doi: 10.48550/arxiv.1603.08516 · pith_short_12: LIU2PE33XUWN · pith_short_16: LIU2PE33XUWNBGEK · pith_short_8: LIU2PE33

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/LIU2PE33XUWNBGEK4GQA3I4QSM \
  | 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: 5a29a7937bbd2cd0988ae1a00da390932c2cdec96732054d8089ce09a8e72dd3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b3e76e929372606adcb4ad33a95c1da2163e99949697ae504260eb6a37a8174",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-03-28T11:07:46Z",
    "title_canon_sha256": "aea030931b0ea7fb5bce2e74370b90006b7733a3b1bb61e85328d07fb2bcf7fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.08516",
    "kind": "arxiv",
    "version": 2
  }
}