Pith Number

pith:PMKDTWWH

pith:2021:PMKDTWWHMUI32QWCLDUHALS2UZ

not attested not anchored not stored refs pending

A Class of Dimension-free Metrics for the Convergence of Empirical Measures

Jiequn Han, Jihao Long, Ruimeng Hu

arxiv:2104.12036 v4 · 2021-04-24 · math.PR · cs.LG · stat.ML

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PMKDTWWHMUI32QWCLDUHALS2UZ}

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	2026-07-05T06:51:16.205554Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b1439dac76511bd42c258e8702e5aa65286d239d109e0075134151177e15e5c

Aliases

arxiv: 2104.12036 · arxiv_version: 2104.12036v4 · doi: 10.48550/arxiv.2104.12036 · pith_short_12: PMKDTWWHMUI3 · pith_short_16: PMKDTWWHMUI32QWC · pith_short_8: PMKDTWWH

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/PMKDTWWHMUI32QWCLDUHALS2UZ \
  | 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: 7b1439dac76511bd42c258e8702e5aa65286d239d109e0075134151177e15e5c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "75e88824f392ddba79b421f32507e12541bac222334476b28fde8001f592f6a9",
    "cross_cats_sorted": [
      "cs.LG",
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2021-04-24T23:27:40Z",
    "title_canon_sha256": "6d14d376c970e236a9fe0e2ce8e270f35e7f5fa69db84692e5d18a65339d231b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2104.12036",
    "kind": "arxiv",
    "version": 4
  }
}