Pith Number

pith:45GMAKHT

pith:2019:45GMAKHTDK5JOYQUD5BV3GFPQC

not attested not anchored not stored refs pending

Random Self-Similar Trees: A mathematical theory of Horton laws

Ilya Zaliapin, Yevgeniy Kovchegov

arxiv:1905.02629 v2 · 2019-05-07 · math.PR · math-ph · math.CO · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{45GMAKHTDK5JOYQUD5BV3GFPQC}

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	2026-05-17T23:45:51.584854Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e74cc028f31aba9762141f435d98af809ccf9f657662687840a546cadb1a66a9

Aliases

arxiv: 1905.02629 · arxiv_version: 1905.02629v2 · doi: 10.48550/arxiv.1905.02629 · pith_short_12: 45GMAKHTDK5J · pith_short_16: 45GMAKHTDK5JOYQU · pith_short_8: 45GMAKHT

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/45GMAKHTDK5JOYQUD5BV3GFPQC \
  | 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: e74cc028f31aba9762141f435d98af809ccf9f657662687840a546cadb1a66a9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "931df8774be2ad463c615300b36baccd51857926dbc3f6bcd08c0bfe6f6e03c0",
    "cross_cats_sorted": [
      "math-ph",
      "math.CO",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-05-07T14:57:55Z",
    "title_canon_sha256": "40dd6817f405c1f37805d48e2c93e2395bf1170e86c7b030429b571e88695062"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.02629",
    "kind": "arxiv",
    "version": 2
  }
}