Pith Number

pith:LWMC3RNJ

pith:2012:LWMC3RNJWKQCWQ7ZHW3ZYC27I2

not attested not anchored not stored refs pending

Galton-Watson trees with vanishing martingale limit

Nadia Sidorova, Nathanael Berestycki, Nina Gantert, Peter Morters

arxiv:1204.3080 v1 · 2012-04-13 · 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{LWMC3RNJWKQCWQ7ZHW3ZYC27I2}

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	2026-05-18T03:57:53.992965Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5d982dc5a9b2a02b43f93db79c0b5f468972cd4390b715d9f1529c836c25f94d

Aliases

arxiv: 1204.3080 · arxiv_version: 1204.3080v1 · doi: 10.48550/arxiv.1204.3080 · pith_short_12: LWMC3RNJWKQC · pith_short_16: LWMC3RNJWKQCWQ7Z · pith_short_8: LWMC3RNJ

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/LWMC3RNJWKQCWQ7ZHW3ZYC27I2 \
  | 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: 5d982dc5a9b2a02b43f93db79c0b5f468972cd4390b715d9f1529c836c25f94d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "76735c1296426ad672dfc1d7ddee161b696b18fba384351a55ce432e2024fa1a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-04-13T19:20:12Z",
    "title_canon_sha256": "7711ad273c5cea8664a522a7533d18c5c90c66337366a6dd87ae468939dd9681"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.3080",
    "kind": "arxiv",
    "version": 1
  }
}