Pith Number

pith:PJV3BCON

pith:2011:PJV3BCONW4BBBZFVBT3IASUGLZ

not attested not anchored not stored refs pending

Ollivier's Ricci curvature, local clustering and curvature dimension inequalities on graphs

J\"urgen Jost, Shiping Liu

arxiv:1103.4037 v3 · 2011-03-21 · math.CO · math.DG · math.MG · 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{PJV3BCONW4BBBZFVBT3IASUGLZ}

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.

Cited by

1 paper in Pith

Elements of finite geometry I

Receipt and verification

First computed	2026-05-18T02:45:05.295472Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a6bb089cdb70210e4b50cf6804a865e7b3d7c24886d1c63e1de28e7225b274b

Aliases

arxiv: 1103.4037 · arxiv_version: 1103.4037v3 · doi: 10.48550/arxiv.1103.4037 · pith_short_12: PJV3BCONW4BB · pith_short_16: PJV3BCONW4BBBZFV · pith_short_8: PJV3BCON

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/PJV3BCONW4BBBZFVBT3IASUGLZ \
  | 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: 7a6bb089cdb70210e4b50cf6804a865e7b3d7c24886d1c63e1de28e7225b274b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ea4074398b00d8ce482ad4d76fdd73a44f534029169c3804c6d03424e534aa0",
    "cross_cats_sorted": [
      "math.DG",
      "math.MG",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-03-21T14:47:36Z",
    "title_canon_sha256": "719fc745f494d815117c11a98173ab45f35c6111842ed2b62a590f2b0c41e8cf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.4037",
    "kind": "arxiv",
    "version": 3
  }
}