Pith Number

pith:XA6ZTXCT

pith:2013:XA6ZTXCT7CD2AGK45LHXRDFX3U

not attested not anchored not stored refs pending

Formation of singularities in solutions to the compressible radiation hydrodynamics equations with vacuum

Shengguo Zhu, Yachun Li

arxiv:1309.7419 v2 · 2013-09-28 · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XA6ZTXCT7CD2AGK45LHXRDFX3U}

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	2026-05-18T03:02:34.348269Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b83d99dc53f887a0195ceacf788cb7dd3f9a563f657220b6758a987d194e7aac

Aliases

arxiv: 1309.7419 · arxiv_version: 1309.7419v2 · doi: 10.48550/arxiv.1309.7419 · pith_short_12: XA6ZTXCT7CD2 · pith_short_16: XA6ZTXCT7CD2AGK4 · pith_short_8: XA6ZTXCT

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/XA6ZTXCT7CD2AGK45LHXRDFX3U \
  | 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: b83d99dc53f887a0195ceacf788cb7dd3f9a563f657220b6758a987d194e7aac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8645369ceced33be1aca0312dda7b2842bbdaf066fb341af18e9145cd01303a9",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-09-28T03:40:35Z",
    "title_canon_sha256": "f149269838a578a0e530cb4fa50bc21396f635672dcea0387200951d565cad33"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.7419",
    "kind": "arxiv",
    "version": 2
  }
}