Pith Number

pith:BKDO2JR5

pith:2011:BKDO2JR5J64CAPWL7UNRBAEEJE

not attested not anchored not stored refs pending

Ricci curvature of finite Markov chains via convexity of the entropy

Jan Maas, Matthias Erbar

arxiv:1111.2687 v2 · 2011-11-11 · math.MG · math.DG · math.FA · 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{BKDO2JR5J64CAPWL7UNRBAEEJE}

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	2026-05-18T01:59:40.306524Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0a86ed263d4fb8203ecbfd1b108084490bddbe6e6deb5862492f4552f30d5411

Aliases

arxiv: 1111.2687 · arxiv_version: 1111.2687v2 · doi: 10.48550/arxiv.1111.2687 · pith_short_12: BKDO2JR5J64C · pith_short_16: BKDO2JR5J64CAPWL · pith_short_8: BKDO2JR5

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/BKDO2JR5J64CAPWL7UNRBAEEJE \
  | 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: 0a86ed263d4fb8203ecbfd1b108084490bddbe6e6deb5862492f4552f30d5411

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23c1db2b38c127507827d0d5073bf19dbeb23a0cac4996a1fa2c7840ebc82eab",
    "cross_cats_sorted": [
      "math.DG",
      "math.FA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2011-11-11T09:12:15Z",
    "title_canon_sha256": "222327f1bc79cef9b789dfc3f49d55927c998f48acd7cdebaaf376ebd6b71a3a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.2687",
    "kind": "arxiv",
    "version": 2
  }
}