Pith Number

pith:5A3RIRBN

pith:2010:5A3RIRBNZDFHNTNF7QYVUKNF5L

not attested not anchored not stored refs pending

On the trace of branching random walks

Itai Benjamini, Sebastian M\"uller

arxiv:1002.2781 v2 · 2010-02-14 · math.PR · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5A3RIRBNZDFHNTNF7QYVUKNF5L}

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	2026-05-18T04:38:59.231207Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e83714442dc8ca76cda5fc315a29a5ead7d33f02189836f5cdd055195b3178b2

Aliases

arxiv: 1002.2781 · arxiv_version: 1002.2781v2 · doi: 10.48550/arxiv.1002.2781 · pith_short_12: 5A3RIRBNZDFH · pith_short_16: 5A3RIRBNZDFHNTNF · pith_short_8: 5A3RIRBN

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/5A3RIRBNZDFHNTNF7QYVUKNF5L \
  | 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: e83714442dc8ca76cda5fc315a29a5ead7d33f02189836f5cdd055195b3178b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "51b2fa2ac5e404dc322052af91a92adf0499626cd61d588ce976de7668cd64f5",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-02-14T22:06:19Z",
    "title_canon_sha256": "38b5f8c91175accf66016bece5dfcca21e3680f4a719c0837edcf5009ffbfe91"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1002.2781",
    "kind": "arxiv",
    "version": 2
  }
}