Pith Number

pith:JWFYA2MC

pith:2011:JWFYA2MCZNIZCOISO4QSMMHJ22

not attested not anchored not stored refs pending

Tokunaga and Horton self-similarity for level set trees of Markov chains

Ilya Zaliapin, Yevgeniy Kovchegov

arxiv:1101.2429 v2 · 2011-01-12 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JWFYA2MCZNIZCOISO4QSMMHJ22}

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	2026-05-18T02:03:40.786555Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4d8b806982cb5191391277212630e9d69fd784998276c31c789d8650561a6a86

Aliases

arxiv: 1101.2429 · arxiv_version: 1101.2429v2 · doi: 10.48550/arxiv.1101.2429 · pith_short_12: JWFYA2MCZNIZ · pith_short_16: JWFYA2MCZNIZCOIS · pith_short_8: JWFYA2MC

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/JWFYA2MCZNIZCOISO4QSMMHJ22 \
  | 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: 4d8b806982cb5191391277212630e9d69fd784998276c31c789d8650561a6a86

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "679f7689953cad9ab5a51e1264fbc9f8f3d6f702c5bdc78ffbc4b3704d2e4413",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-01-12T19:26:07Z",
    "title_canon_sha256": "67833f52b4170e331261f5eaee7d85febd3119d42dff0aed9c4fa3979b6d664c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.2429",
    "kind": "arxiv",
    "version": 2
  }
}