Pith Number

pith:AH654KD7

pith:2013:AH654KD7BIDVN4MUXFVC4IGQKO

not attested not anchored not stored refs pending

The vertex-cut-tree of Galton-Watson trees converging to a stable tree

Daphn\'e Dieuleveut

arxiv:1312.5525 v2 · 2013-12-19 · 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{AH654KD7BIDVN4MUXFVC4IGQKO}

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	2026-05-18T01:09:32.395416Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

01fdde287f0a0756f194b96a2e20d053aba5bad657a5f04b7201ec2881d3606d

Aliases

arxiv: 1312.5525 · arxiv_version: 1312.5525v2 · doi: 10.48550/arxiv.1312.5525 · pith_short_12: AH654KD7BIDV · pith_short_16: AH654KD7BIDVN4MU · pith_short_8: AH654KD7

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/AH654KD7BIDVN4MUXFVC4IGQKO \
  | 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: 01fdde287f0a0756f194b96a2e20d053aba5bad657a5f04b7201ec2881d3606d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9500b714135193c8e20d8007a7a685eb6106b65f28491ff85f535f05d39e9e13",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-12-19T13:01:35Z",
    "title_canon_sha256": "c91d26c91dbfd7987814ea06e987c36bd830bb9ed85a2b798b8497b2357bf81b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.5525",
    "kind": "arxiv",
    "version": 2
  }
}