Pith Number

pith:ODUD547N

pith:2015:ODUD547NU4UTOPQIJIYEKFAMD6

not attested not anchored not stored refs pending

Critical Multi-Type Galton-Watson Trees Conditioned to be Large

Hongsong Guo, Jean-Fran\c{c}ois Delmas (CERMICS), Romain Abraham (MAPMO)

arxiv:1511.01721 v2 · 2015-11-05 · 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{ODUD547NU4UTOPQIJIYEKFAMD6}

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	2026-05-18T01:03:50.927344Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

70e83ef3eda729373e084a3045140c1f978971072f3228f3a346dea40f999c24

Aliases

arxiv: 1511.01721 · arxiv_version: 1511.01721v2 · doi: 10.48550/arxiv.1511.01721 · pith_short_12: ODUD547NU4UT · pith_short_16: ODUD547NU4UTOPQI · pith_short_8: ODUD547N

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/ODUD547NU4UTOPQIJIYEKFAMD6 \
  | 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: 70e83ef3eda729373e084a3045140c1f978971072f3228f3a346dea40f999c24

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a99c31a4f4ce132c0e2c4cc892157176cd37cdfddbb3baf59f2164422cb85fa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-11-05T12:52:54Z",
    "title_canon_sha256": "4280f9bb839393cafeb78a82228abf6d94f95349e8f9e3cf5df9101729c82e0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.01721",
    "kind": "arxiv",
    "version": 2
  }
}