Pith Number

pith:W7FI3EO4

pith:2017:W7FI3EO4J2TKC3OGLJA5WGOQZM

not attested not anchored not stored refs pending

Limit theorems for supercritical MBPRE with linear fractional offspring distributions

Minzhi Liu, Vladimir Vatutin, Wenming Hong

arxiv:1710.08724 v1 · 2017-10-24 · 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{W7FI3EO4J2TKC3OGLJA5WGOQZM}

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	2026-05-18T00:32:03.972073Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7ca8d91dc4ea6a16dc65a41db19d0cb2986dd70d70f1cc18a64cad2266f6929

Aliases

arxiv: 1710.08724 · arxiv_version: 1710.08724v1 · doi: 10.48550/arxiv.1710.08724 · pith_short_12: W7FI3EO4J2TK · pith_short_16: W7FI3EO4J2TKC3OG · pith_short_8: W7FI3EO4

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/W7FI3EO4J2TKC3OGLJA5WGOQZM \
  | 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: b7ca8d91dc4ea6a16dc65a41db19d0cb2986dd70d70f1cc18a64cad2266f6929

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ced51f9e0ee12ce69b6e2f9e87d4f5f9de12d7407ad75eb835e2bfd4e04009c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-10-24T12:14:13Z",
    "title_canon_sha256": "e8713f665f404bc5a32a78684db4bcd9cbc012f5494ed776da8cfcd17334974e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1710.08724",
    "kind": "arxiv",
    "version": 1
  }
}