Pith Number

pith:ZEFOCRN3

pith:2012:ZEFOCRN3LTQVMLN3OWPN2IHAOI

not attested not anchored not stored refs pending

Singularities of solutions to compressible Euler equations with vacuum

Qingtian Zhang, Yi Du, Zhen Lei

arxiv:1203.2396 v2 · 2012-03-12 · 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{ZEFOCRN3LTQVMLN3OWPN2IHAOI}

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	2026-05-18T03:59:28.790188Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c90ae145bb5ce1562dbb759edd20e07238df6287d9649dc87cb23016a44ca6c1

Aliases

arxiv: 1203.2396 · arxiv_version: 1203.2396v2 · doi: 10.48550/arxiv.1203.2396 · pith_short_12: ZEFOCRN3LTQV · pith_short_16: ZEFOCRN3LTQVMLN3 · pith_short_8: ZEFOCRN3

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/ZEFOCRN3LTQVMLN3OWPN2IHAOI \
  | 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: c90ae145bb5ce1562dbb759edd20e07238df6287d9649dc87cb23016a44ca6c1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "65562452f35cb8ec75446333fa40d1f8eac40642a5bc0f529e57bde5be1ae7b6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-03-12T02:52:37Z",
    "title_canon_sha256": "c08bca703cf03c8c3077059df63f2fd0a889f5778b7470b7ae68ee711b391324"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.2396",
    "kind": "arxiv",
    "version": 2
  }
}