Pith Number

pith:TLCCAYDE

pith:2014:TLCCAYDEFQITDQMRSV53AR2ZPF

not attested not anchored not stored refs pending

Secret Hidden in Navier-Stokes Equations: Singularity and Criterion of Turbulent Transition

Hua-Shu Dou

arxiv:1409.0086 v2 · 2014-08-30 · physics.flu-dyn · math.AP · nlin.CD

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TLCCAYDEFQITDQMRSV53AR2ZPF}

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	2026-05-18T02:30:31.656865Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ac42060642c1131c191957bb047597970eaa56a029ca126c92912da76caa8c4

Aliases

arxiv: 1409.0086 · arxiv_version: 1409.0086v2 · doi: 10.48550/arxiv.1409.0086 · pith_short_12: TLCCAYDEFQIT · pith_short_16: TLCCAYDEFQITDQMR · pith_short_8: TLCCAYDE

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/TLCCAYDEFQITDQMRSV53AR2ZPF \
  | 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: 9ac42060642c1131c191957bb047597970eaa56a029ca126c92912da76caa8c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86e45f188e381e43df942d68592349a4f315315f3a4f83eea01dade281de464f",
    "cross_cats_sorted": [
      "math.AP",
      "nlin.CD"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.flu-dyn",
    "submitted_at": "2014-08-30T05:38:50Z",
    "title_canon_sha256": "b54023e37d4cdcec9059e06cf8e5df1a5c32d1f5329a641922f76b131dd0f411"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.0086",
    "kind": "arxiv",
    "version": 2
  }
}