Pith Number

pith:DGVPLQ2K

pith:2011:DGVPLQ2K7ATLBR2YUFCO236N7S

not attested not anchored not stored refs pending

Stationary Navier-Stokes Equations with Critically Singular External Forces: Existence and Stability Results

Nguyen Cong Phuc, Tuoc Van Phan

arxiv:1111.2787 v2 · 2011-11-11 · 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{DGVPLQ2K7ATLBR2YUFCO236N7S}

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	2026-05-18T03:29:37.773069Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

19aaf5c34af826b0c758a144ed6fcdfc8b4759f2619f785eb3fae2d43de36a28

Aliases

arxiv: 1111.2787 · arxiv_version: 1111.2787v2 · doi: 10.48550/arxiv.1111.2787 · pith_short_12: DGVPLQ2K7ATL · pith_short_16: DGVPLQ2K7ATLBR2Y · pith_short_8: DGVPLQ2K

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/DGVPLQ2K7ATLBR2YUFCO236N7S \
  | 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: 19aaf5c34af826b0c758a144ed6fcdfc8b4759f2619f785eb3fae2d43de36a28

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0784a79acedbe9489369e60c2295ed7c6d34a2fa8c03474619e9645fe78bd4d8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-11-11T16:20:23Z",
    "title_canon_sha256": "33232dffe56168b010391671f88501198c9d6a1fbb3626d89447c0bb656d265d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.2787",
    "kind": "arxiv",
    "version": 2
  }
}