Pith Number

pith:JNVV26H7

pith:2016:JNVV26H7CERJPKQO663LWHHCGG

not attested not anchored not stored refs pending

Kinetic and mean field description of Gibrat's law

Giuseppe Toscani

arxiv:1606.04796 v1 · 2016-04-06 · q-fin.GN · math.PR · 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{JNVV26H7CERJPKQO663LWHHCGG}

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	2026-05-18T01:10:47.255631Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b6b5d78ff112297aa0ef7b6bb1ce231a11cf0b8c19f7220b20adb747efa1708

Aliases

arxiv: 1606.04796 · arxiv_version: 1606.04796v1 · doi: 10.48550/arxiv.1606.04796 · pith_short_12: JNVV26H7CERJ · pith_short_16: JNVV26H7CERJPKQO · pith_short_8: JNVV26H7

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/JNVV26H7CERJPKQO663LWHHCGG \
  | 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: 4b6b5d78ff112297aa0ef7b6bb1ce231a11cf0b8c19f7220b20adb747efa1708

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5dd7625dc50b85f6d9ae957e7d835955fc47d20634264e5e880a21719ed9b070",
    "cross_cats_sorted": [
      "math.PR",
      "physics.soc-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "q-fin.GN",
    "submitted_at": "2016-04-06T13:21:14Z",
    "title_canon_sha256": "d0169bcb88ff3df0a3d971801d43224765dfe97f2e21c816049d511c1e207919"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.04796",
    "kind": "arxiv",
    "version": 1
  }
}