Pith Number

pith:U2CZL7TS

pith:2008:U2CZL7TS4GHI2QMBYBFTTQOVXR

not attested not anchored not stored refs pending

Phi-entropy inequalities for diffusion semigroups

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

arxiv:0812.0800 v3 · 2008-12-03 · 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{U2CZL7TS4GHI2QMBYBFTTQOVXR}

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	2026-05-18T03:13:08.677205Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a68595fe72e18e8d4181c04b39c1d5bc56d137a39f6c7f8a5045ea64ffc143f2

Aliases

arxiv: 0812.0800 · arxiv_version: 0812.0800v3 · doi: 10.48550/arxiv.0812.0800 · pith_short_12: U2CZL7TS4GHI · pith_short_16: U2CZL7TS4GHI2QMB · pith_short_8: U2CZL7TS

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/U2CZL7TS4GHI2QMBYBFTTQOVXR \
  | 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: a68595fe72e18e8d4181c04b39c1d5bc56d137a39f6c7f8a5045ea64ffc143f2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2461c1ec55308f072a42e64bc6ea31293b92044879ca51b467193c934d0d712d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2008-12-03T20:31:20Z",
    "title_canon_sha256": "219479edbe397100e65a12ae0a18c9bbd91772cc3efb95ea8d6ae6a6858d8de0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.0800",
    "kind": "arxiv",
    "version": 3
  }
}