Pith Number

pith:6W6GLYFG

pith:2010:6W6GLYFGH2Z42OTHY634IL3EVA

not attested not anchored not stored refs pending

From chemical Langevin equations to Fokker-Planck equation: application of Hodge decomposition and Klein-Kramers equation

Weihua Mu, Xiaoqing Li, Zhongcan Ou-Yang

arxiv:1009.3648 v1 · 2010-09-19 · 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{6W6GLYFGH2Z42OTHY634IL3EVA}

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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	2026-05-18T02:05:21.778588Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f5bc65e0a63eb3cd3a67c7b7c42f64a816d37511a967be03f648dd1a1c2267c8

Aliases

arxiv: 1009.3648 · arxiv_version: 1009.3648v1 · doi: 10.48550/arxiv.1009.3648 · pith_short_12: 6W6GLYFGH2Z4 · pith_short_16: 6W6GLYFGH2Z42OTH · pith_short_8: 6W6GLYFG

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/6W6GLYFGH2Z42OTHY634IL3EVA \
  | 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: f5bc65e0a63eb3cd3a67c7b7c42f64a816d37511a967be03f648dd1a1c2267c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "79507f600ec15368aa3f8c1f9f006a43f7d992bf27a3598159a62c8e7a322aa7",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2010-09-19T16:53:29Z",
    "title_canon_sha256": "db4434e498d0675c714bd352442a61f3aa1d9bd3bc19b3c9e3d30015af6ca59e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.3648",
    "kind": "arxiv",
    "version": 1
  }
}