Pith Number

pith:4YKQD2ZJ

pith:2009:4YKQD2ZJLMQZM3AIBVHYYD4I52

not attested not anchored not stored refs pending

The number of degrees of freedom of three-dimensional Navier--Stokes turbulence

Chuong V. Tran

arxiv:0912.2000 v1 · 2009-12-10 · physics.flu-dyn

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4YKQD2ZJLMQZM3AIBVHYYD4I52}

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	2026-05-18T02:10:24.837708Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e61501eb295b21966c080d4f8c0f88eebebc4a7e9703a31f7569f974ae648a8a

Aliases

arxiv: 0912.2000 · arxiv_version: 0912.2000v1 · doi: 10.48550/arxiv.0912.2000 · pith_short_12: 4YKQD2ZJLMQZ · pith_short_16: 4YKQD2ZJLMQZM3AI · pith_short_8: 4YKQD2ZJ

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/4YKQD2ZJLMQZM3AIBVHYYD4I52 \
  | 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: e61501eb295b21966c080d4f8c0f88eebebc4a7e9703a31f7569f974ae648a8a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "21469f7f3cb699d33d990934e857d73da05f1240622df3a3b98ab8e2268b6523",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.flu-dyn",
    "submitted_at": "2009-12-10T14:12:49Z",
    "title_canon_sha256": "6cb2b8119ab70739341ac9421ba4398e93d2098e8699f2a246ff785e906b34a5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.2000",
    "kind": "arxiv",
    "version": 1
  }
}