Pith Number

pith:GCJES5KP

pith:2013:GCJES5KPBTJVOBDNCBUA6DFYUK

not attested not anchored not stored refs pending

Local limits of conditioned Galton-Watson trees I: the infinite spine case

Jean-Francois Delmas (CERMICS), Romain Abraham (MAPMO)

arxiv:1304.4035 v4 · 2013-04-15 · 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{GCJES5KPBTJVOBDNCBUA6DFYUK}

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	2026-05-18T02:48:47.053310Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

309249754f0cd357046d10680f0cb8a2b56b198b0f329b3b46d013e7b5c27b4b

Aliases

arxiv: 1304.4035 · arxiv_version: 1304.4035v4 · doi: 10.48550/arxiv.1304.4035 · pith_short_12: GCJES5KPBTJV · pith_short_16: GCJES5KPBTJVOBDN · pith_short_8: GCJES5KP

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/GCJES5KPBTJVOBDNCBUA6DFYUK \
  | 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: 309249754f0cd357046d10680f0cb8a2b56b198b0f329b3b46d013e7b5c27b4b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b875c8a0c7bee091a9f6c5e081d52c6157aaa1154a2e339ef7de175d672c9bc3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-04-15T09:46:23Z",
    "title_canon_sha256": "d72950f1b87720365eec10219c4185a8d8fa14f39440ce7d01dbfef6f098ff62"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.4035",
    "kind": "arxiv",
    "version": 4
  }
}