Pith Number

pith:45DZ2WVT

pith:2010:45DZ2WVTO5EXKV2WKZZNUIGWRW

not attested not anchored not stored refs pending

Convergence in $L^p$ and its exponential rate for a branching process in a random environment

Chunmao Huang, Quansheng Liu

arxiv:1011.0533 v2 · 2010-11-02 · 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{45DZ2WVTO5EXKV2WKZZNUIGWRW}

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	2026-05-18T02:19:42.889476Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e7479d5ab377497557565672da20d68d9e86caded5b77ed44094f0ba5d87c8b6

Aliases

arxiv: 1011.0533 · arxiv_version: 1011.0533v2 · doi: 10.48550/arxiv.1011.0533 · pith_short_12: 45DZ2WVTO5EX · pith_short_16: 45DZ2WVTO5EXKV2W · pith_short_8: 45DZ2WVT

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/45DZ2WVTO5EXKV2WKZZNUIGWRW \
  | 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: e7479d5ab377497557565672da20d68d9e86caded5b77ed44094f0ba5d87c8b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "16a6de59c45ff0e56beaaf70f50811b49121aa153e1b74849048834816a2472f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-11-02T07:57:56Z",
    "title_canon_sha256": "b06685c2495390366a54cb8dc228bda5de54157a3e3d9b4a461d79ea9254b8d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.0533",
    "kind": "arxiv",
    "version": 2
  }
}