Pith Number

pith:SGHQTNNK

pith:2012:SGHQTNNKGZTMJ7B73KFSFNIDYQ

not attested not anchored not stored refs pending

On Harnack inequalities and optimal transportation

Dominique Bakry (IUF, IMT), Ivan Gentil (ICJ), Michel Ledoux (IUF

arxiv:1210.4650 v4 · 2012-10-17 · 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{SGHQTNNKGZTMJ7B73KFSFNIDYQ}

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	2026-05-18T03:19:11.542106Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

918f09b5aa3666c4fc3fda8b22b503c428c258ed6647bd881f4667b8513a825b

Aliases

arxiv: 1210.4650 · arxiv_version: 1210.4650v4 · doi: 10.48550/arxiv.1210.4650 · pith_short_12: SGHQTNNKGZTM · pith_short_16: SGHQTNNKGZTMJ7B7 · pith_short_8: SGHQTNNK

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/SGHQTNNKGZTMJ7B73KFSFNIDYQ \
  | 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: 918f09b5aa3666c4fc3fda8b22b503c428c258ed6647bd881f4667b8513a825b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7fc03e1bc6c725d562a7672c5ca96157768835c51ea62feddc3dac2220d5d288",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-10-17T07:35:28Z",
    "title_canon_sha256": "ba165344e9e3a66849b4690760b9bb4dfc4523ad65de97f4242eb48c5697a7f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.4650",
    "kind": "arxiv",
    "version": 4
  }
}