Pith Number

pith:3QJ2IQFZ

pith:2012:3QJ2IQFZZIMS6MTEPIUBHAPRTP

not attested not anchored not stored refs pending

Well-posedness of The Prandtl Equation in Sobolev Spaces

Chao-Jiang Xu (LMRS), Radjesvarane Alexandre (IRENAV), Tong Yang (Pr.), Ya-Guang Wang

arxiv:1203.5991 v1 · 2012-03-27 · 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{3QJ2IQFZZIMS6MTEPIUBHAPRTP}

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	2026-05-18T03:59:12.790747Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dc13a440b9ca192f32647a281381f19be80863acb53c2f504e1fbabc5d6d8343

Aliases

arxiv: 1203.5991 · arxiv_version: 1203.5991v1 · doi: 10.48550/arxiv.1203.5991 · pith_short_12: 3QJ2IQFZZIMS · pith_short_16: 3QJ2IQFZZIMS6MTE · pith_short_8: 3QJ2IQFZ

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/3QJ2IQFZZIMS6MTEPIUBHAPRTP \
  | 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: dc13a440b9ca192f32647a281381f19be80863acb53c2f504e1fbabc5d6d8343

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a624406742e758f88eb932f70e66f7b3f1b4a6e1e12d42d5369de84c137d882e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-03-27T14:57:07Z",
    "title_canon_sha256": "4941d18083a2bd3898f01b916ff93a7d63a373fd7a79bbfa9c78c2699014b8ea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.5991",
    "kind": "arxiv",
    "version": 1
  }
}