Pith Number

pith:FYAPT2AX

pith:2007:FYAPT2AXEMMLLTMVUIMUMQXPJL

not attested not anchored not stored refs pending

Ricci curvature of Markov chains on metric spaces

Yann Ollivier

arxiv:math/0701886 v4 · 2007-01-30 · math.PR · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FYAPT2AXEMMLLTMVUIMUMQXPJL}

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	2026-07-04T15:03:19.663429Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2e00f9e8172318b5cd95a2194642ef4ad2be4897b15cea714d743dbc8a3456aa

Aliases

arxiv: math/0701886 · arxiv_version: math/0701886v4 · doi: 10.48550/arxiv.math/0701886 · pith_short_12: FYAPT2AXEMML · pith_short_16: FYAPT2AXEMMLLTMV · pith_short_8: FYAPT2AX

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/FYAPT2AXEMMLLTMVUIMUMQXPJL \
  | 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: 2e00f9e8172318b5cd95a2194642ef4ad2be4897b15cea714d743dbc8a3456aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b914f61c951ec7e58c0c12aecc9f1928666763e9d3083ee53bc2c840987e3e52",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2007-01-30T16:41:12Z",
    "title_canon_sha256": "468d9a7682dfb74522a49166b66058de0772765c5e743213b2158cf7960532b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0701886",
    "kind": "arxiv",
    "version": 4
  }
}