Pith Number

pith:UIARGSBC

pith:2010:UIARGSBCCDHWZQ6KQITASEQSQG

not attested not anchored not stored refs pending

Multitype branching processes with immigration in random environment and polling systems

Vladimir Vatutin

arxiv:1004.4973 v1 · 2010-04-28 · 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{UIARGSBCCDHWZQ6KQITASEQSQG}

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	2026-05-18T02:24:15.557446Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a20113482210cf6cc3ca8226091212819583309f38c91c4b84e7465612dbdab3

Aliases

arxiv: 1004.4973 · arxiv_version: 1004.4973v1 · doi: 10.48550/arxiv.1004.4973 · pith_short_12: UIARGSBCCDHW · pith_short_16: UIARGSBCCDHWZQ6K · pith_short_8: UIARGSBC

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/UIARGSBCCDHWZQ6KQITASEQSQG \
  | 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: a20113482210cf6cc3ca8226091212819583309f38c91c4b84e7465612dbdab3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2ea10f95efea10ad679bb71e7e8da6c637a2ad5b557072072c929b46bc41fdf4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-04-28T08:27:52Z",
    "title_canon_sha256": "7caae5de389c442f2704df2f598181ccfcd485098c0eed17380972f8acfe37f6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.4973",
    "kind": "arxiv",
    "version": 1
  }
}