Pith Number

pith:LBTNQJWB

pith:2013:LBTNQJWBB4Y56RMKKA722KUHJM

not attested not anchored not stored refs pending

Almost sure existence of Navier-Stokes Equations with randomized data in the whole space

Cheng Yu, Dehua Wang, Robin Ming Chen, Song Yao

arxiv:1308.1588 v4 · 2013-08-07 · 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{LBTNQJWBB4Y56RMKKA722KUHJM}

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	2026-05-18T03:08:46.786144Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5866d826c10f31df458a503fad2a874b300a110f998f2ad64ac622c470bb2782

Aliases

arxiv: 1308.1588 · arxiv_version: 1308.1588v4 · doi: 10.48550/arxiv.1308.1588 · pith_short_12: LBTNQJWBB4Y5 · pith_short_16: LBTNQJWBB4Y56RMK · pith_short_8: LBTNQJWB

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/LBTNQJWBB4Y56RMKKA722KUHJM \
  | 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: 5866d826c10f31df458a503fad2a874b300a110f998f2ad64ac622c470bb2782

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "84814d0d9a2dc13e86c2609336f0c0ecee02402bd579e39a37df9cb467bb6c1a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-08-07T14:49:36Z",
    "title_canon_sha256": "5cf3e30a5f60e7c528dbe629640ba0ec2eb5071960eecbdcc88cb7e9c7eb458f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.1588",
    "kind": "arxiv",
    "version": 4
  }
}