Pith Number

pith:7IFYR3TP

pith:2011:7IFYR3TPJRWH5ECVHD4WM3GQDZ

not attested not anchored not stored refs pending

Predicted and Verified Deviations from Zipf's law in Ecology of Competing Products

Didier Sornette, Ryohei Hisano, Takayuki Mizuno

arxiv:1101.5888 v4 · 2011-01-31 · physics.soc-ph · cs.SI

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7IFYR3TPJRWH5ECVHD4WM3GQDZ}

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	2026-05-18T02:22:41.847536Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fa0b88ee6f4c6c7e905538f9666cd01e545ca79252945a381f5b03985babaa27

Aliases

arxiv: 1101.5888 · arxiv_version: 1101.5888v4 · doi: 10.48550/arxiv.1101.5888 · pith_short_12: 7IFYR3TPJRWH · pith_short_16: 7IFYR3TPJRWH5ECV · pith_short_8: 7IFYR3TP

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/7IFYR3TPJRWH5ECVHD4WM3GQDZ \
  | 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: fa0b88ee6f4c6c7e905538f9666cd01e545ca79252945a381f5b03985babaa27

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "343ba9cc81cfe56828f44b01d17e28aa0e6ad46de7dd49016c37c0b6e5138b24",
    "cross_cats_sorted": [
      "cs.SI"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.soc-ph",
    "submitted_at": "2011-01-31T09:55:24Z",
    "title_canon_sha256": "ff58dcdb22a599acc8f945901fa934d0b6c84026e7813c4f15445adc928ce082"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.5888",
    "kind": "arxiv",
    "version": 4
  }
}