Pith Number

pith:WB2LFEUQ

pith:2015:WB2LFEUQ2OG7NEL4IILG7SLHMK

not attested not anchored not stored refs pending

On the emergence of the Navier-Stokes-$\alpha$ model for turbulent channel flows

Bingsheng Zhang, Ciprian Foias, Jing Tian

arxiv:1511.00989 v2 · 2015-10-31 · math.AP · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WB2LFEUQ2OG7NEL4IILG7SLHMK}

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	2026-05-18T01:04:22.223374Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b074b29290d38df6917c42166fc96762a91f6973a79ad3e9b8e551228a8dd639

Aliases

arxiv: 1511.00989 · arxiv_version: 1511.00989v2 · doi: 10.48550/arxiv.1511.00989 · pith_short_12: WB2LFEUQ2OG7 · pith_short_16: WB2LFEUQ2OG7NEL4 · pith_short_8: WB2LFEUQ

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/WB2LFEUQ2OG7NEL4IILG7SLHMK \
  | 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: b074b29290d38df6917c42166fc96762a91f6973a79ad3e9b8e551228a8dd639

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23a1b4035a1bdb8219fc310c695058d9de1cc8e3ed6cb352be1a190ec02a6253",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-10-31T21:34:56Z",
    "title_canon_sha256": "914861caed600dbad68be03d58dd785b1148e12a12125fd2214d8c8e539ba305"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.00989",
    "kind": "arxiv",
    "version": 2
  }
}