Pith Number

pith:NJFRIA3Z

pith:2015:NJFRIA3Z7CEEHJ4QCG33ACZYPT

not attested not anchored not stored refs pending

Stationary solutions of the Vlasov-Fokker-Planck equation: existence, characterization and phase-transition

Julian Tugaut, Manh Hong Duong

arxiv:1505.01212 v3 · 2015-05-05 · math.AP · math-ph · math.MP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NJFRIA3Z7CEEHJ4QCG33ACZYPT}

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	2026-05-18T01:35:38.048836Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a4b140379f88843a79011b7b00b387ce793e1486e31e95b4f12ffde03268d85

Aliases

arxiv: 1505.01212 · arxiv_version: 1505.01212v3 · doi: 10.48550/arxiv.1505.01212 · pith_short_12: NJFRIA3Z7CEE · pith_short_16: NJFRIA3Z7CEEHJ4Q · pith_short_8: NJFRIA3Z

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/NJFRIA3Z7CEEHJ4QCG33ACZYPT \
  | 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: 6a4b140379f88843a79011b7b00b387ce793e1486e31e95b4f12ffde03268d85

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "874a0b0f00ed09f3525436e65a2ea0ad837107bb51956f04931bc81bfba91bee",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-05-05T22:46:14Z",
    "title_canon_sha256": "731434e7fafd7641b9d31a0d1b7a29ad63616debf4cd2c8656fc00c9c39ca86f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.01212",
    "kind": "arxiv",
    "version": 3
  }
}