Pith Number

pith:Z6NQS2FR

pith:2011:Z6NQS2FRQ2UQ65ITCHVE6QDAAT

not attested not anchored not stored refs pending

A Lagrangian approach for the incompressible Navier-Stokes equations with variable density

Piotr Bogus{\l}aw Mucha, Rapha\"el Danchin

arxiv:1107.2763 v1 · 2011-07-14 · 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{Z6NQS2FRQ2UQ65ITCHVE6QDAAT}

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	2026-05-18T01:09:25.388999Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf9b0968b186a90f751311ea4f406004f2e717b2ede4e72c8571d3d9ee45cfc8

Aliases

arxiv: 1107.2763 · arxiv_version: 1107.2763v1 · doi: 10.48550/arxiv.1107.2763 · pith_short_12: Z6NQS2FRQ2UQ · pith_short_16: Z6NQS2FRQ2UQ65IT · pith_short_8: Z6NQS2FR

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/Z6NQS2FRQ2UQ65ITCHVE6QDAAT \
  | 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: cf9b0968b186a90f751311ea4f406004f2e717b2ede4e72c8571d3d9ee45cfc8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fc6f77bff9b9fd239e352318e51a2cf8ee0688ae61ae60b264c5dbf75d44f124",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-07-14T09:36:54Z",
    "title_canon_sha256": "2a52091c34121665891b4efcead41e8c75e6d9cfc38701cf1616e818072569de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.2763",
    "kind": "arxiv",
    "version": 1
  }
}