Pith Number

pith:EZVZBZCL

pith:2010:EZVZBZCLBNMOXPATS7Q2U5Z4C6

not attested not anchored not stored refs pending

Sub-Gaussian tail bounds for the width and height of conditioned Galton--Watson trees

Louigi Addario-Berry, Luc Devroye, Svante Janson

arxiv:1011.4121 v1 · 2010-11-18 · 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{EZVZBZCLBNMOXPATS7Q2U5Z4C6}

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	2026-05-18T02:47:16.406805Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

266b90e44b0b58ebbc1397e1aa773c17a626353e3fe844e247e9507ba59f4be1

Aliases

arxiv: 1011.4121 · arxiv_version: 1011.4121v1 · doi: 10.48550/arxiv.1011.4121 · pith_short_12: EZVZBZCLBNMO · pith_short_16: EZVZBZCLBNMOXPAT · pith_short_8: EZVZBZCL

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/EZVZBZCLBNMOXPATS7Q2U5Z4C6 \
  | 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: 266b90e44b0b58ebbc1397e1aa773c17a626353e3fe844e247e9507ba59f4be1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e85504dd28f82d0d5bb5d5d3412c84cddc973198a9ea121977b9fc606e1a284d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-11-18T01:39:06Z",
    "title_canon_sha256": "8e55ec5a8c9123bb8749d677c67c3083aaacac7e25b227584be68ceeb112c6c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.4121",
    "kind": "arxiv",
    "version": 1
  }
}