Pith Number

pith:DPTZVWJP

pith:2010:DPTZVWJPBCUZUE26QN5Z3LQJHM

not attested not anchored not stored refs pending

Phi-entropy inequalities and Fokker-Planck equations

Fran\c{c}ois Bolley (CEREMADE), Ivan Gentil (CEREMADE)

arxiv:1002.4478 v1 · 2010-02-24 · 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{DPTZVWJPBCUZUE26QN5Z3LQJHM}

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	2026-05-18T03:13:00.729426Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1be79ad92f08a99a135e837b9dae093b0466aa0342d16a35f0395b43ba680ed3

Aliases

arxiv: 1002.4478 · arxiv_version: 1002.4478v1 · doi: 10.48550/arxiv.1002.4478 · pith_short_12: DPTZVWJPBCUZ · pith_short_16: DPTZVWJPBCUZUE26 · pith_short_8: DPTZVWJP

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/DPTZVWJPBCUZUE26QN5Z3LQJHM \
  | 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: 1be79ad92f08a99a135e837b9dae093b0466aa0342d16a35f0395b43ba680ed3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "61c4cb7454ec3336a24c4ad079c6f8eb9084a6f5c8e6d98d8775d2ad46d9a4d2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-02-24T06:17:54Z",
    "title_canon_sha256": "0438e1ed8b2eda91a3afbc8e050d91bac6c46f05b1b45158f361f1aea30b1f7b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1002.4478",
    "kind": "arxiv",
    "version": 1
  }
}