Pith Number

pith:PT4VJ4NY

pith:2006:PT4VJ4NYNBXB35JK7NAKLLIOII

not attested not anchored not stored refs pending

The Modulo 1 Central Limit Theorem and Benford's Law for Products

Mark J. Nigrini, Steven J. Miller

arxiv:math/0607686 v2 · 2006-07-26 · math.PR · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PT4VJ4NYNBXB35JK7NAKLLIOII}

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	2026-05-18T04:40:56.379122Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7cf954f1b8686e1df52afb40a5ad0e4239e47ccaca25c70c2803cb14d36efb0f

Aliases

arxiv: math/0607686 · arxiv_version: math/0607686v2 · doi: 10.48550/arxiv.math/0607686 · pith_short_12: PT4VJ4NYNBXB · pith_short_16: PT4VJ4NYNBXB35JK · pith_short_8: PT4VJ4NY

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/PT4VJ4NYNBXB35JK7NAKLLIOII \
  | 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: 7cf954f1b8686e1df52afb40a5ad0e4239e47ccaca25c70c2803cb14d36efb0f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba88ef26b18353f266e847509880c6d7e28c22b0383a5cb6f34d6530b9fce9b7",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2006-07-26T20:18:50Z",
    "title_canon_sha256": "90b71fcd747f23f6cc6dedc40fc3e9e2fcd8867482348875dd603d1ca955bd51"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0607686",
    "kind": "arxiv",
    "version": 2
  }
}