Pith Number

pith:V4UYHFD2

pith:2026:V4UYHFD2KDK7EBFCJLJQ57ZIBS

not attested not anchored not stored refs pending

Numerical Validation of Lyapunov-Liouville Theory and Non-Diffusive Closures in Decaying Isotropic Fluid and Scalar Turbulence

Nicola de Divitiis

arxiv:2607.22105 v1 · 2026-07-24 · 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{V4UYHFD2KDK7EBFCJLJQ57ZIBS}

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	2026-07-27T01:20:48.523865Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

af2983947a50d5f204a24ad30eff280cbca1a4861a5f4cf1f56c613bd3a8e253

Aliases

arxiv: 2607.22105 · arxiv_version: 2607.22105v1 · doi: 10.48550/arxiv.2607.22105 · pith_short_12: V4UYHFD2KDK7 · pith_short_16: V4UYHFD2KDK7EBFC · pith_short_8: V4UYHFD2

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/V4UYHFD2KDK7EBFCJLJQ57ZIBS \
  | 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: af2983947a50d5f204a24ad30eff280cbca1a4861a5f4cf1f56c613bd3a8e253

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac1ad1d990c0ab3b849fbb7f817e9e2ddf55a7489d923a65f706cccad9bd76ae",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.flu-dyn",
    "submitted_at": "2026-07-24T08:57:21Z",
    "title_canon_sha256": "eb2a47543604816b21e1c4d54fd23593b5ffe2958edabd4b8d7c531fea13fda1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.22105",
    "kind": "arxiv",
    "version": 1
  }
}