Pith Number

pith:ZAPY26FL

pith:2013:ZAPY26FLK2IXYZ3ETIET7HAYGN

not attested not anchored not stored refs pending

Generalised central limit theorems for growth rate distribution of complex systems

Hayafumi Watanabe, Hideki Takayasu, Misako Takayasu

arxiv:1301.2728 v4 · 2013-01-12 · physics.soc-ph · physics.data-an · q-fin.GN · stat.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZAPY26FLK2IXYZ3ETIET7HAYGN}

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	2026-05-18T01:52:12.977196Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c81f8d78ab56917c67649a093f9c183342afe4735d7143ccf8e46d789345d490

Aliases

arxiv: 1301.2728 · arxiv_version: 1301.2728v4 · doi: 10.48550/arxiv.1301.2728 · pith_short_12: ZAPY26FLK2IX · pith_short_16: ZAPY26FLK2IXYZ3E · pith_short_8: ZAPY26FL

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/ZAPY26FLK2IXYZ3ETIET7HAYGN \
  | 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: c81f8d78ab56917c67649a093f9c183342afe4735d7143ccf8e46d789345d490

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bde3cb6a0a8728138f0e3b9e34fac796da8f78763adb656784b479652c52467b",
    "cross_cats_sorted": [
      "physics.data-an",
      "q-fin.GN",
      "stat.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.soc-ph",
    "submitted_at": "2013-01-12T22:57:32Z",
    "title_canon_sha256": "45ce854b2ebbeadb0bb358a34bd0a8a04facebfc48ac90c4660f17b7f1449b45"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.2728",
    "kind": "arxiv",
    "version": 4
  }
}