Pith Number

pith:V63DS4CZ

pith:2013:V63DS4CZ4MAGZPAJUQGHVKLXSW

not attested not anchored not stored refs pending

Existence of Smooth Solutions of the Navier-Stokes Equations

Dongsheng Li

arxiv:1308.3909 v1 · 2013-08-19 · 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{V63DS4CZ4MAGZPAJUQGHVKLXSW}

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	2026-05-18T03:15:35.310335Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

afb6397059e3006cbc09a40c7aa977959a6672917377848e70e31d11f1f77b66

Aliases

arxiv: 1308.3909 · arxiv_version: 1308.3909v1 · doi: 10.48550/arxiv.1308.3909 · pith_short_12: V63DS4CZ4MAG · pith_short_16: V63DS4CZ4MAGZPAJ · pith_short_8: V63DS4CZ

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/V63DS4CZ4MAGZPAJUQGHVKLXSW \
  | 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: afb6397059e3006cbc09a40c7aa977959a6672917377848e70e31d11f1f77b66

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9d2f6b2f51beb37d75fe106611192d9d5e0d86e72d998ce8fe08d6f2225da30c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-08-19T01:38:55Z",
    "title_canon_sha256": "bfb09126a2e6216bc02c515888f56c7039af841dbe3f746427250d30fe3b2cc2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.3909",
    "kind": "arxiv",
    "version": 1
  }
}