Pith Number

pith:UQJPEE46

pith:2013:UQJPEE46WGQD2BXBPLHATODKNE

not attested not anchored not stored refs pending

Liouville-type theorems for the forced Euler equations and the Navier-Stokes equations

Dongho Chae

arxiv:1306.5839 v1 · 2013-06-25 · 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{UQJPEE46WGQD2BXBPLHATODKNE}

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	2026-05-18T01:49:08.280616Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a412f2139eb1a03d06e17ace09b86a6920faaadbd42a26b0b31672147302a3b6

Aliases

arxiv: 1306.5839 · arxiv_version: 1306.5839v1 · doi: 10.48550/arxiv.1306.5839 · pith_short_12: UQJPEE46WGQD · pith_short_16: UQJPEE46WGQD2BXB · pith_short_8: UQJPEE46

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/UQJPEE46WGQD2BXBPLHATODKNE \
  | 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: a412f2139eb1a03d06e17ace09b86a6920faaadbd42a26b0b31672147302a3b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "023feb2c3986c354e5a2fedcd09158a38661c3357db02043f7454001bd9a9c0d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-06-25T03:15:39Z",
    "title_canon_sha256": "4ff8aa226fb504ff66d69c35c98e7f5b23758964ddfafad85f65720a914ceb19"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.5839",
    "kind": "arxiv",
    "version": 1
  }
}