Pith Number

pith:6HLJCO76

pith:2004:6HLJCO76JOF75YBD23LQZPJUCJ

not attested not anchored not stored refs pending

Ricci curvature for metric-measure spaces via optimal transport

Cedric Villani, John Lott

arxiv:math/0412127 v4 · 2004-12-07 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6HLJCO76JOF75YBD23LQZPJUCJ}

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	2026-07-04T14:50:08.832076Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f1d6913bfe4b8bfee023d6d70cbd34126f6d52c9081bb22e0f11308671501c31

Aliases

arxiv: math/0412127 · arxiv_version: math/0412127v4 · doi: 10.48550/arxiv.math/0412127 · pith_short_12: 6HLJCO76JOF7 · pith_short_16: 6HLJCO76JOF75YBD · pith_short_8: 6HLJCO76

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/6HLJCO76JOF75YBD23LQZPJUCJ \
  | 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: f1d6913bfe4b8bfee023d6d70cbd34126f6d52c9081bb22e0f11308671501c31

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6cf0525ed42999d629a87dcadd895e3a67e8660ffda503ed18ddb8631adf1df2",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "2004-12-07T05:06:33Z",
    "title_canon_sha256": "1dfda65d62f33d05f637535b24c99c9846c1b997652f6980447db8c6580921b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0412127",
    "kind": "arxiv",
    "version": 4
  }
}