Pith Number

pith:ZVM2IDSL

pith:2009:ZVM2IDSLZJ3NPF4V6YFK2PEMST

not attested not anchored not stored refs pending

Gibrat's law for cities: uniformly most powerful unbiased test of the Pareto against the lognormal

D. Sornette, V. Pisarenko, Y. Malevergne

arxiv:0909.1281 v1 · 2009-09-07 · physics.data-an · physics.soc-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZVM2IDSLZJ3NPF4V6YFK2PEMST}

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	2026-05-18T02:11:58.945344Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd59a40e4bca76d79795f60aad3c8c94eb0d3d5f1415e5478f91698715b93d3a

Aliases

arxiv: 0909.1281 · arxiv_version: 0909.1281v1 · doi: 10.48550/arxiv.0909.1281 · pith_short_12: ZVM2IDSLZJ3N · pith_short_16: ZVM2IDSLZJ3NPF4V · pith_short_8: ZVM2IDSL

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/ZVM2IDSLZJ3NPF4V6YFK2PEMST \
  | 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: cd59a40e4bca76d79795f60aad3c8c94eb0d3d5f1415e5478f91698715b93d3a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4947b8aef90779201f08e676432ef2fdb0e31094e7666120593dcd6c97118423",
    "cross_cats_sorted": [
      "physics.soc-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.data-an",
    "submitted_at": "2009-09-07T16:54:46Z",
    "title_canon_sha256": "63483391665f6dd1be82b35920049d4a05f46efdd7b983fe166a73422ec05dab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.1281",
    "kind": "arxiv",
    "version": 1
  }
}