Pith Number

pith:3PPOAFPZ

pith:2015:3PPOAFPZVVQJ7ZAKUZRZRJKRUR

not attested not anchored not stored refs pending

Long time well-posdness of the Prandtl equations in Sobolev space

Chao-Jiang Xu (LMRS), Xu Zhang

arxiv:1511.04850 v6 · 2015-11-16 · 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{3PPOAFPZVVQJ7ZAKUZRZRJKRUR}

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	2026-05-18T01:15:23.058806Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dbdee015f9ad609fe40aa66398a551a466de7843e650355f086c6b2a061899bf

Aliases

arxiv: 1511.04850 · arxiv_version: 1511.04850v6 · doi: 10.48550/arxiv.1511.04850 · pith_short_12: 3PPOAFPZVVQJ · pith_short_16: 3PPOAFPZVVQJ7ZAK · pith_short_8: 3PPOAFPZ

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/3PPOAFPZVVQJ7ZAKUZRZRJKRUR \
  | 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: dbdee015f9ad609fe40aa66398a551a466de7843e650355f086c6b2a061899bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "35f1c769182a8c9b371753e46ca4ad4911772229ad5892753f53210812df31a5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-11-16T07:40:59Z",
    "title_canon_sha256": "c541e241394ba49a1e2eff628848f6369e4a3c487a03a1989366629589940ba6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.04850",
    "kind": "arxiv",
    "version": 6
  }
}