Pith Number

pith:Z7RWFJAP

pith:2012:Z7RWFJAPQLX4ZXLCAEPKUISRXY

not attested not anchored not stored refs pending

Global weak solutions to the Navier-Stokes-Vlasov equations

Cheng Yu

arxiv:1204.6540 v2 · 2012-04-30 · 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{Z7RWFJAPQLX4ZXLCAEPKUISRXY}

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	2026-05-18T03:39:52.963861Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cfe362a40f82efccdd62011eaa2251be2b2f8cc7e7ac5b5622f46c6f6f2b8e26

Aliases

arxiv: 1204.6540 · arxiv_version: 1204.6540v2 · doi: 10.48550/arxiv.1204.6540 · pith_short_12: Z7RWFJAPQLX4 · pith_short_16: Z7RWFJAPQLX4ZXLC · pith_short_8: Z7RWFJAP

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/Z7RWFJAPQLX4ZXLCAEPKUISRXY \
  | 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: cfe362a40f82efccdd62011eaa2251be2b2f8cc7e7ac5b5622f46c6f6f2b8e26

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c27aa363cbb9985be897ffe46e6e61530c3a38bcd32a84d61b44e75fc0bc2c8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-04-30T03:07:16Z",
    "title_canon_sha256": "7489cf8eb5a149d3a9cef2f48db4bb1611232ad70b850b17488a6439b5231292"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.6540",
    "kind": "arxiv",
    "version": 2
  }
}