Pith Number

pith:JZ6CLJHG

pith:2012:JZ6CLJHGVCKVFMOVVF22IYE3DH

not attested not anchored not stored refs pending

Subgeometric rates of convergence of Markov processes in the Wasserstein metric

Oleg Butkovsky

arxiv:1211.4273 v3 · 2012-11-18 · 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{JZ6CLJHGVCKVFMOVVF22IYE3DH}

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	2026-05-18T02:56:05.348334Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4e7c25a4e6a89552b1d5a975a4609b19f0507fb0c2f7fc3b9f685a1873cf0def

Aliases

arxiv: 1211.4273 · arxiv_version: 1211.4273v3 · doi: 10.48550/arxiv.1211.4273 · pith_short_12: JZ6CLJHGVCKV · pith_short_16: JZ6CLJHGVCKVFMOV · pith_short_8: JZ6CLJHG

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/JZ6CLJHGVCKVFMOVVF22IYE3DH \
  | 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: 4e7c25a4e6a89552b1d5a975a4609b19f0507fb0c2f7fc3b9f685a1873cf0def

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "182c8b84ec05092dfe922eb9925a2a4c9d9dc7fa8ced0a203d3c497bacd594b4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-11-18T23:40:22Z",
    "title_canon_sha256": "f39ad2ae0bffe4fc70b607eb599983c138e3b6bca87adc3fcd779cfc249fbbfb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.4273",
    "kind": "arxiv",
    "version": 3
  }
}