Pith Number

pith:YDOY3VRZ

pith:2011:YDOY3VRZZI3KFS3VFVAIHAFUQR

not attested not anchored not stored refs pending

Speed of the biased random walk on a Galton--Watson tree

elie aidekon

arxiv:1111.4313 v4 · 2011-11-18 · 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{YDOY3VRZZI3KFS3VFVAIHAFUQR}

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	2026-05-18T02:21:28.884117Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c0dd8dd639ca36a2cb752d408380b484653afd0fd806359ca499447ad266ad2a

Aliases

arxiv: 1111.4313 · arxiv_version: 1111.4313v4 · doi: 10.48550/arxiv.1111.4313 · pith_short_12: YDOY3VRZZI3K · pith_short_16: YDOY3VRZZI3KFS3V · pith_short_8: YDOY3VRZ

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/YDOY3VRZZI3KFS3VFVAIHAFUQR \
  | 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: c0dd8dd639ca36a2cb752d408380b484653afd0fd806359ca499447ad266ad2a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "da6c09a5940a25b001ca10cf3db656cb87977e3df87adf690a9600be8b238f94",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-11-18T09:56:32Z",
    "title_canon_sha256": "410e23596de9cde24ecab7c26459d9289950c2c39c8176853a1cb815dccdeaea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.4313",
    "kind": "arxiv",
    "version": 4
  }
}