Pith Number

pith:2RZTZ5GO

pith:2010:2RZTZ5GOKNSPG4FYXV26SCOGX2

not attested not anchored not stored refs pending

The Wigner-Fokker-Planck equation: Stationary states and large-time behavior

Anton Arnold, Christof Sparber, Clement Mouhot, Irene M. Gamba, Maria Pia Gualdani, Stephane Mischler

arxiv:1010.2791 v3 · 2010-10-13 · math.AP · math-ph · math.MP · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2RZTZ5GOKNSPG4FYXV26SCOGX2}

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	2026-05-18T04:04:15.350042Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d4733cf4ce5364f370b8bd75e909c6bea35be9cc997ac9ccf3612ea7680ed61a

Aliases

arxiv: 1010.2791 · arxiv_version: 1010.2791v3 · doi: 10.48550/arxiv.1010.2791 · pith_short_12: 2RZTZ5GOKNSP · pith_short_16: 2RZTZ5GOKNSPG4FY · pith_short_8: 2RZTZ5GO

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/2RZTZ5GOKNSPG4FYXV26SCOGX2 \
  | 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: d4733cf4ce5364f370b8bd75e909c6bea35be9cc997ac9ccf3612ea7680ed61a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "403e063d2805e5182f1a2dad8d5dc1ea5119b09c1efe4fd8d80d3fadbe88a62f",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-10-13T23:14:33Z",
    "title_canon_sha256": "41f47bff5aeddafe88ca80a6295c92176aa210ed13362c34ecff7ac9bc68d859"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.2791",
    "kind": "arxiv",
    "version": 3
  }
}