Pith Number

pith:7BNQVCEH

pith:2022:7BNQVCEH3PQ4QRDS5R4UZMY4FR

not attested not anchored not stored refs pending

Rate of convergence of the smoothed empirical Wasserstein distance

Adam Block, Alexander Rakhlin, Yury Polyanskiy, Zeyu Jia

arxiv:2205.02128 v4 · 2022-05-04 · math.PR · cs.IT · math.IT · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7BNQVCEH3PQ4QRDS5R4UZMY4FR}

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	2026-07-05T10:11:11.449116Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f85b0a8887dbe1c84472ec794cb31c2c44dfdcedca3cc664f99dc3cd4c38e660

Aliases

arxiv: 2205.02128 · arxiv_version: 2205.02128v4 · doi: 10.48550/arxiv.2205.02128 · pith_short_12: 7BNQVCEH3PQ4 · pith_short_16: 7BNQVCEH3PQ4QRDS · pith_short_8: 7BNQVCEH

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/7BNQVCEH3PQ4QRDS5R4UZMY4FR \
  | 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: f85b0a8887dbe1c84472ec794cb31c2c44dfdcedca3cc664f99dc3cd4c38e660

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb8781d16731a1eba669694cf1fb953ab25bc2603f8fe49326c36f392193c4a6",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2022-05-04T15:31:51Z",
    "title_canon_sha256": "f48f55775606c02017fa3735bad0ee78046d9696378a034d8e81ef7e951fddc3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2205.02128",
    "kind": "arxiv",
    "version": 4
  }
}