Pith Number

pith:4RATOW3L

pith:2014:4RATOW3LTUT33R3ZSAACFGPREL

not attested not anchored not stored refs pending

Approximation of 2D Euler Equations by the Second-Grade Fluid Equations with Dirichlet Boundary Conditions

Aibin Zang, Edriss S. Titi, Helena J. Nussenzveig Lopes, Milton C. Lopes Filho

arxiv:1412.6587 v1 · 2014-12-20 · 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{4RATOW3LTUT33R3ZSAACFGPREL}

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	2026-05-18T01:55:07.584283Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e441375b6b9d27bdc77990002299f122d9c8397deda0d8a013632de3a1657008

Aliases

arxiv: 1412.6587 · arxiv_version: 1412.6587v1 · doi: 10.48550/arxiv.1412.6587 · pith_short_12: 4RATOW3LTUT3 · pith_short_16: 4RATOW3LTUT33R3Z · pith_short_8: 4RATOW3L

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/4RATOW3LTUT33R3ZSAACFGPREL \
  | 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: e441375b6b9d27bdc77990002299f122d9c8397deda0d8a013632de3a1657008

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4a23cd35e2ffd577f67ac64b3d3a1c58fc87d748b727d6059e9c92c1ff992d4",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2014-12-20T03:12:19Z",
    "title_canon_sha256": "1d2c56d0fb1938926a3e3818527c6fd753b1c1f909aa5546d2c6b95118b775a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.6587",
    "kind": "arxiv",
    "version": 1
  }
}