Pith Number

pith:5II2ZAIN

pith:2012:5II2ZAINV52QTWPTA6XJT36YF6

not attested not anchored not stored refs pending

On the duality between jump processes on ultrametric spaces and random walks on trees

Wolfgang Woess

arxiv:1211.7216 v1 · 2012-11-30 · 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{5II2ZAINV52QTWPTA6XJT36YF6}

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	2026-05-18T03:39:31.257653Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ea11ac810daf7509d9f307ae99efd82fa9901f3d78f78250fa0c05901f4976c3

Aliases

arxiv: 1211.7216 · arxiv_version: 1211.7216v1 · doi: 10.48550/arxiv.1211.7216 · pith_short_12: 5II2ZAINV52Q · pith_short_16: 5II2ZAINV52QTWPT · pith_short_8: 5II2ZAIN

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/5II2ZAINV52QTWPTA6XJT36YF6 \
  | 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: ea11ac810daf7509d9f307ae99efd82fa9901f3d78f78250fa0c05901f4976c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7984e709e24e543d95b6b9b31ca70419956c9f218c00134ef13d9da582ee13db",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-11-30T11:30:41Z",
    "title_canon_sha256": "7a42671c00bd923bd1b11648f2f4dc74263f9d570c993e93ee712a86c8435110"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.7216",
    "kind": "arxiv",
    "version": 1
  }
}