Pith Number

pith:ZAQ7KHXH

pith:2003:ZAQ7KHXHYSKXZCAFRUOBIWMJSD

not attested not anchored not stored refs pending

Universality of Critical Behaviour in a Class of Recurrent Random Walks

Ostap Hryniv, Yvan Velenik

arxiv:math/0310217 v1 · 2003-10-15 · math.PR · math-ph · 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{ZAQ7KHXHYSKXZCAFRUOBIWMJSD}

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	2026-05-18T04:14:46.413879Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c821f51ee7c4957c88058d1c14598990f4334e480d95d4c1db61662efd945bee

Aliases

arxiv: math/0310217 · arxiv_version: math/0310217v1 · doi: 10.48550/arxiv.math/0310217 · pith_short_12: ZAQ7KHXHYSKX · pith_short_16: ZAQ7KHXHYSKXZCAF · pith_short_8: ZAQ7KHXH

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/ZAQ7KHXHYSKXZCAFRUOBIWMJSD \
  | 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: c821f51ee7c4957c88058d1c14598990f4334e480d95d4c1db61662efd945bee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "57bb4935ca27804dd59dd678118892448a1bfd9303dc42b65a01f302815545a6",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2003-10-15T12:38:16Z",
    "title_canon_sha256": "3a61bdfb82b159be505b260e78d98a640a7901fe3ba41e459ecdc37d3acb0c67"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0310217",
    "kind": "arxiv",
    "version": 1
  }
}