Pith Number

pith:CG3Y6VV2

pith:2026:CG3Y6VV2UEE7GV2H3W2PASULMO

not attested not anchored not stored refs pending

Mutual Information second order expansion is the Pearson's chi-square statistic

Marius Marinescu

arxiv:2607.18425 v1 · 2026-07-20 · 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{CG3Y6VV2UEE7GV2H3W2PASULMO}

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	2026-07-22T00:22:47.739328Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

11b78f56baa109f35747ddb4f04a8b63942a090ef65efee23fae6e35f97f0651

Aliases

arxiv: 2607.18425 · arxiv_version: 2607.18425v1 · doi: 10.48550/arxiv.2607.18425 · pith_short_12: CG3Y6VV2UEE7 · pith_short_16: CG3Y6VV2UEE7GV2H · pith_short_8: CG3Y6VV2

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/CG3Y6VV2UEE7GV2H3W2PASULMO \
  | 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: 11b78f56baa109f35747ddb4f04a8b63942a090ef65efee23fae6e35f97f0651

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9cce8904f095c06a7af5d149005e4f6a66249f478858f0601b7ba9dfe610eded",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-07-20T18:14:46Z",
    "title_canon_sha256": "1a7cf31e8d90b0e3ddb24aef0924ca28777ae919f35a837240dac5fde8eb3be3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.18425",
    "kind": "arxiv",
    "version": 1
  }
}