Pith Number

pith:F32UKBJR

pith:2018:F32UKBJRFTLP27PFQFTFZIX7RR

not attested not anchored not stored refs pending

Seven proofs of the Pearson Chi-squared independence test and its graphical interpretation

Eric Benhamou, Valentin Melot

arxiv:1808.09171 v3 · 2018-08-28 · 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{F32UKBJRFTLP27PFQFTFZIX7RR}

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	2026-05-18T00:06:36.637536Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ef54505312cd6fd7de581665ca2ff8c687b05d06064e710ae7a6775eb46ee24

Aliases

arxiv: 1808.09171 · arxiv_version: 1808.09171v3 · doi: 10.48550/arxiv.1808.09171 · pith_short_12: F32UKBJRFTLP · pith_short_16: F32UKBJRFTLP27PF · pith_short_8: F32UKBJR

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/F32UKBJRFTLP27PFQFTFZIX7RR \
  | 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: 2ef54505312cd6fd7de581665ca2ff8c687b05d06064e710ae7a6775eb46ee24

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "27bf64e28d90f2f031a9ed750355936f9ad9dafce5ddda11e22d3114414ac00a",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2018-08-28T08:43:11Z",
    "title_canon_sha256": "768cad4a4f9593284024b6ceaf1df5b0b94ab128cca8f0fd5d3a19a534b64556"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.09171",
    "kind": "arxiv",
    "version": 3
  }
}