Pith Number

pith:ZK4IFIVU

pith:2015:ZK4IFIVUHW53SUZPJPTTSNOMKX

not attested not anchored not stored refs pending

Local limits of galton-watson trees conditioned on the number of protected nodes

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

arxiv:1509.02350 v2 · 2015-09-08 · 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{ZK4IFIVUHW53SUZPJPTTSNOMKX}

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	2026-05-18T01:16:18.194584Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cab882a2b43dbbb9532f4be73935cc55ef7b19d61b40abec68b4877c5598a8ca

Aliases

arxiv: 1509.02350 · arxiv_version: 1509.02350v2 · doi: 10.48550/arxiv.1509.02350 · pith_short_12: ZK4IFIVUHW53 · pith_short_16: ZK4IFIVUHW53SUZP · pith_short_8: ZK4IFIVU

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/ZK4IFIVUHW53SUZPJPTTSNOMKX \
  | 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: cab882a2b43dbbb9532f4be73935cc55ef7b19d61b40abec68b4877c5598a8ca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4c1e1b95727298c68a7b380d1cf8d9ad983f71a89e607a4f73cdcedb0f67c48",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-09-08T13:04:39Z",
    "title_canon_sha256": "656ef21562bc27562b09746948b4065f1623a0edffd23037833366d8717484ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.02350",
    "kind": "arxiv",
    "version": 2
  }
}