Pith Number

pith:P7GWUFOP

pith:2018:P7GWUFOP7WWZQKGZNMXESLJWPQ

not attested not anchored not stored refs pending

Exponential Decay for Lions-Feireisl's Weak Solutions to the Barotropic Compressible Navier-Stokes Equations in 3D Bounded Domains

Xiaoding Shi, Yan-fang Peng

arxiv:1805.06352 v1 · 2018-05-16 · 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{P7GWUFOP7WWZQKGZNMXESLJWPQ}

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	2026-05-18T00:15:48.007091Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7fcd6a15cffdad9828d96b2e492d367c21ce4e247239cbd8779cb8be05071cbd

Aliases

arxiv: 1805.06352 · arxiv_version: 1805.06352v1 · doi: 10.48550/arxiv.1805.06352 · pith_short_12: P7GWUFOP7WWZ · pith_short_16: P7GWUFOP7WWZQKGZ · pith_short_8: P7GWUFOP

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/P7GWUFOP7WWZQKGZNMXESLJWPQ \
  | 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: 7fcd6a15cffdad9828d96b2e492d367c21ce4e247239cbd8779cb8be05071cbd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4a9a5fcc76adf94d2a262b1dcc7ea942b671408f12b3697a0cf47f04f6d6982c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-05-16T14:50:55Z",
    "title_canon_sha256": "de6a1799ef51be0424723c67d9f094b8d68718e0288b5f6e4f0530f6b55c9528"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.06352",
    "kind": "arxiv",
    "version": 1
  }
}