Pith Number

pith:5DIPTVHV

pith:2013:5DIPTVHVY4IOUOY6LOTTBB5AXO

not attested not anchored not stored refs pending

Dobrushin's ergodicity coefficient for Markov operators on cones

Stephane Gaubert, Zheng Qu

arxiv:1307.4649 v3 · 2013-07-17 · math.FA · math.OA · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5DIPTVHVY4IOUOY6LOTTBB5AXO}

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	2026-05-18T02:30:15.880957Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e8d0f9d4f5c710ea3b1e5ba73087a0bba1286ae7e44e4811cadc7ded26dadf93

Aliases

arxiv: 1307.4649 · arxiv_version: 1307.4649v3 · doi: 10.48550/arxiv.1307.4649 · pith_short_12: 5DIPTVHVY4IO · pith_short_16: 5DIPTVHVY4IOUOY6 · pith_short_8: 5DIPTVHV

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/5DIPTVHVY4IOUOY6LOTTBB5AXO \
  | 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: e8d0f9d4f5c710ea3b1e5ba73087a0bba1286ae7e44e4811cadc7ded26dadf93

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c359d01ccbd5bdfc7ed014b6a7680bfa5d48fe2d3dbaab3d3ee2fc4282d27034",
    "cross_cats_sorted": [
      "math.OA",
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-07-17T14:30:28Z",
    "title_canon_sha256": "eb5b4ba2ca2e227ea781926056e30bd921bbb20d44b476ab837d46e03b600391"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.4649",
    "kind": "arxiv",
    "version": 3
  }
}