Pith Number

pith:WBMZY5EF

pith:2015:WBMZY5EFQ6A2MC637HYBR3E6YZ

not attested not anchored not stored refs pending

Liouville type theorems for the steady axially symmetric Navier-Stokes and magnetohydrodynamic equations

Dongho Chae, Shangkun Weng

arxiv:1512.03491 v2 · 2015-12-11 · 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{WBMZY5EFQ6A2MC637HYBR3E6YZ}

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	2026-05-18T01:19:05.416959Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0599c74858781a60bdbf9f018ec9ec6708d5586acacde7b69a1820fe31fa08f

Aliases

arxiv: 1512.03491 · arxiv_version: 1512.03491v2 · doi: 10.48550/arxiv.1512.03491 · pith_short_12: WBMZY5EFQ6A2 · pith_short_16: WBMZY5EFQ6A2MC63 · pith_short_8: WBMZY5EF

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/WBMZY5EFQ6A2MC637HYBR3E6YZ \
  | 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: b0599c74858781a60bdbf9f018ec9ec6708d5586acacde7b69a1820fe31fa08f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a3e93684fbd66cfc78e53f6a6ea8b34ce35496b5b7d99aab80d1162f7292ecf9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-12-11T00:25:32Z",
    "title_canon_sha256": "2fe9b46085938e7ef7daf9a42c062d95886d9878144171e2cc9cf7cb7f8d9314"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.03491",
    "kind": "arxiv",
    "version": 2
  }
}