Pith Number

pith:I2GKXKRG

pith:2021:I2GKXKRGW3HN6E6M3X4N36OPJB

not attested not anchored not stored refs pending

Smooth test for equality of copulas

Denys Pommeret, Yves Isma\"el Ngounou Bakam

arxiv:2112.05623 v3 · 2021-12-10 · math.ST · stat.AP · stat.ME · 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{I2GKXKRGW3HN6E6M3X4N36OPJB}

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	2026-07-05T07:20:47.088112Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

468cabaa26b6cedf13ccddf8ddf9cf4868a17363e53405c3efc02a8ead55441e

Aliases

arxiv: 2112.05623 · arxiv_version: 2112.05623v3 · doi: 10.48550/arxiv.2112.05623 · pith_short_12: I2GKXKRGW3HN · pith_short_16: I2GKXKRGW3HN6E6M · pith_short_8: I2GKXKRG

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/I2GKXKRGW3HN6E6M3X4N36OPJB \
  | 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: 468cabaa26b6cedf13ccddf8ddf9cf4868a17363e53405c3efc02a8ead55441e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07602fc852bc95bf5de7f91cdc50a2fd919cea78552cf0446056759fe0de006b",
    "cross_cats_sorted": [
      "stat.AP",
      "stat.ME",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2021-12-10T15:59:00Z",
    "title_canon_sha256": "ec1441fd3bf142654e917aa90f167c7b2f71ad56f624e7a621daff3422ab3ae7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.05623",
    "kind": "arxiv",
    "version": 3
  }
}