Pith Number

pith:FDVCKQGJ

pith:2017:FDVCKQGJH2G2T4YVAVMOWR3VUQ

not attested not anchored not stored refs pending

Asymptotic properties of expansive Galton-Watson trees

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

arxiv:1712.04650 v1 · 2017-12-13 · 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{FDVCKQGJH2G2T4YVAVMOWR3VUQ}

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	2026-05-18T00:28:03.885723Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

28ea2540c93e8da9f3150558eb4775a4273f284f927f951b8fc37ef251e221e0

Aliases

arxiv: 1712.04650 · arxiv_version: 1712.04650v1 · doi: 10.48550/arxiv.1712.04650 · pith_short_12: FDVCKQGJH2G2 · pith_short_16: FDVCKQGJH2G2T4YV · pith_short_8: FDVCKQGJ

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/FDVCKQGJH2G2T4YVAVMOWR3VUQ \
  | 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: 28ea2540c93e8da9f3150558eb4775a4273f284f927f951b8fc37ef251e221e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f9d6c6d7f943a528d72df8dd7dcfd374bd6ed9b5a2087adb5c3c8ee334603077",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-12-13T08:18:51Z",
    "title_canon_sha256": "ac5f36770706ae5732080f7bf57476eea48ad7c92125d5b7e2750ee577c12a92"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.04650",
    "kind": "arxiv",
    "version": 1
  }
}