Pith Number

pith:YQ2BJJH4

pith:2016:YQ2BJJH4UPHLEAQSL3FH6EX2Z4

not attested not anchored not stored refs pending

On the Liouville type theorems for self-similar solutions to the Navier-Stokes equations

Dongho Chae, Joerg Wolf

arxiv:1609.06962 v1 · 2016-09-22 · 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{YQ2BJJH4UPHLEAQSL3FH6EX2Z4}

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	2026-05-18T00:45:48.362606Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c43414a4fca3ceb202125eca7f12facf1438b2cff0313fd8a972d9ce02ba2983

Aliases

arxiv: 1609.06962 · arxiv_version: 1609.06962v1 · doi: 10.48550/arxiv.1609.06962 · pith_short_12: YQ2BJJH4UPHL · pith_short_16: YQ2BJJH4UPHLEAQS · pith_short_8: YQ2BJJH4

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/YQ2BJJH4UPHLEAQSL3FH6EX2Z4 \
  | 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: c43414a4fca3ceb202125eca7f12facf1438b2cff0313fd8a972d9ce02ba2983

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca979cde1ad52ec926f2c96f12a13bedf52b77e55dbed1667e3b9bc0791e6714",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-09-22T13:22:18Z",
    "title_canon_sha256": "df5b9e17e9df319f1016bb43b2eeedf136df91413cd25e458388d39d359bb083"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.06962",
    "kind": "arxiv",
    "version": 1
  }
}