Pith Number

pith:22A3PQQX

pith:2010:22A3PQQXFZRQTJRUVGSZNML55C

not attested not anchored not stored refs pending

Central limit theorem for biased random walk on multi-type Galton-Watson trees

Amir Dembo, Nike Sun

arxiv:1011.4056 v2 · 2010-11-17 · 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{22A3PQQXFZRQTJRUVGSZNML55C}

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	2026-05-18T03:56:22.789059Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d681b7c2172e6309a634a9a596b17de8833eb0eae7fc56ed90d1f7f15fdcc7e6

Aliases

arxiv: 1011.4056 · arxiv_version: 1011.4056v2 · doi: 10.48550/arxiv.1011.4056 · pith_short_12: 22A3PQQXFZRQ · pith_short_16: 22A3PQQXFZRQTJRU · pith_short_8: 22A3PQQX

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/22A3PQQXFZRQTJRUVGSZNML55C \
  | 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: d681b7c2172e6309a634a9a596b17de8833eb0eae7fc56ed90d1f7f15fdcc7e6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6a6f4b21d660ea11ce906573b049bbf48eb0091601a04a4d25327b5c7989e747",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-11-17T20:49:39Z",
    "title_canon_sha256": "3b04a6a38f13ebe68b8fdcdcfba0e4901a13ecb2a051728c829973ad970186f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.4056",
    "kind": "arxiv",
    "version": 2
  }
}