Pith Number

pith:YWTGGGC3

pith:2013:YWTGGGC372NRDG3ZPFBOYIZOLT

not attested not anchored not stored refs pending

Navier-Stokes equation and forward-backward stochastic differential system in the Besov spaces

Ana Bela Cruzeiro, Xin Chen, Zhongmin Qian

arxiv:1305.0647 v2 · 2013-05-03 · math.AP · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YWTGGGC372NRDG3ZPFBOYIZOLT}

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	2026-05-18T03:24:41.138821Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c5a663185bfe9b119b797942ec232e5cda82d105408c92f39f56259f90f80681

Aliases

arxiv: 1305.0647 · arxiv_version: 1305.0647v2 · doi: 10.48550/arxiv.1305.0647 · pith_short_12: YWTGGGC372NR · pith_short_16: YWTGGGC372NRDG3Z · pith_short_8: YWTGGGC3

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/YWTGGGC372NRDG3ZPFBOYIZOLT \
  | 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: c5a663185bfe9b119b797942ec232e5cda82d105408c92f39f56259f90f80681

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a5021b19f735330d163572cca8988f3abdb8b718719f34a5c57a7c8b5803d254",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-05-03T09:14:41Z",
    "title_canon_sha256": "2ff10f1239313cdffe53618c0493d1fe66faa6ec2b63f64101b1e7ec60769781"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.0647",
    "kind": "arxiv",
    "version": 2
  }
}