Pith Number

pith:PSZ3UJR4

pith:2002:PSZ3UJR4JK2AR76FJMPRKXDPO2

not attested not anchored not stored refs pending

Entropy and the Law of Small Numbers

Ioannis Kontoyiannis, Oliver Johnson, Peter Harremoes

arxiv:math/0211020 v2 · 2002-11-01 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PSZ3UJR4JK2AR76FJMPRKXDPO2}

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	2026-05-18T04:38:59.449716Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7cb3ba263c4ab408ffc54b1f155c6f7698bb35d33122c5cbd0479f4ef93e3ed5

Aliases

arxiv: math/0211020 · arxiv_version: math/0211020v2 · doi: 10.48550/arxiv.math/0211020 · pith_short_12: PSZ3UJR4JK2A · pith_short_16: PSZ3UJR4JK2AR76F · pith_short_8: PSZ3UJR4

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/PSZ3UJR4JK2AR76FJMPRKXDPO2 \
  | 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: 7cb3ba263c4ab408ffc54b1f155c6f7698bb35d33122c5cbd0479f4ef93e3ed5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7ac191fe63c8316039147da4db7c121cc1b307c9f8d6a996994038e0d406006d",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2002-11-01T17:21:52Z",
    "title_canon_sha256": "ed2f494e3b1f075da58c534a276cc96147f4c76c5350c078d38c918a4498fc38"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0211020",
    "kind": "arxiv",
    "version": 2
  }
}