Pith Number

pith:AZIOI5GM

pith:2012:AZIOI5GMY3WJRX7GOHM3P2UUNY

not attested not anchored not stored refs pending

An Entropic Proof of Chang's Inequality

Alexander Russell, Cristopher Moore, Russell Impagliazzo

arxiv:1205.0263 v2 · 2012-05-01 · cs.CC · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AZIOI5GMY3WJRX7GOHM3P2UUNY}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T03:55:35.117305Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0650e474ccc6ec98dfe671d9b7ea946e137772b5234382e145b39fb546c5c303

Aliases

arxiv: 1205.0263 · arxiv_version: 1205.0263v2 · doi: 10.48550/arxiv.1205.0263 · pith_short_12: AZIOI5GMY3WJ · pith_short_16: AZIOI5GMY3WJRX7G · pith_short_8: AZIOI5GM

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/AZIOI5GMY3WJRX7GOHM3P2UUNY \
  | 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: 0650e474ccc6ec98dfe671d9b7ea946e137772b5234382e145b39fb546c5c303

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "25a9e4524fd614b4e375285ee910dfbf38ee5f3e994afd971fbecc2975e1a2d8",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2012-05-01T21:13:05Z",
    "title_canon_sha256": "bec8b2eb26991539bd23eafc84c9abd49e54b17c01a2239162d603c14f885888"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.0263",
    "kind": "arxiv",
    "version": 2
  }
}