Pith Number

pith:4IMNP3EF

pith:2012:4IMNP3EFVGGT7X3NWBRQR62F46

not attested not anchored not stored refs pending

Global solutions to the three-dimensional full compressible Navier-Stokes equations with vacuum at infinity in some classes of large data

Changjiang Zhu, Huanyao Wen

arxiv:1208.1199 v2 · 2012-08-06 · 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{4IMNP3EFVGGT7X3NWBRQR62F46}

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	2026-05-18T00:50:23.917174Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e218d7ec85a98d3fdf6db06308fb45e78fb79702b910b5bc677d6c5acde09492

Aliases

arxiv: 1208.1199 · arxiv_version: 1208.1199v2 · doi: 10.48550/arxiv.1208.1199 · pith_short_12: 4IMNP3EFVGGT · pith_short_16: 4IMNP3EFVGGT7X3N · pith_short_8: 4IMNP3EF

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/4IMNP3EFVGGT7X3NWBRQR62F46 \
  | 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: e218d7ec85a98d3fdf6db06308fb45e78fb79702b910b5bc677d6c5acde09492

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef969fb50bef9876b018911a7b587308f1d9c3f99cb40a0aa075b9bad6c85d7a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-08-06T16:12:19Z",
    "title_canon_sha256": "b8b76e129414d91b2a9213adf5b073c40096d189d37ec32c8bcfb0999ec776c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.1199",
    "kind": "arxiv",
    "version": 2
  }
}