Pith Number

pith:W2K2FIFH

pith:2010:W2K2FIFHDWPIFTMLT5IHC3CFDT

not attested not anchored not stored refs pending

Limit theorems for weakly subcritical branching processes in random environment

C. Boeinghoff, G. Kersting, V.A. Vatutin, V.I. Afanasyev

arxiv:1001.1672 v2 · 2010-01-11 · 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{W2K2FIFHDWPIFTMLT5IHC3CFDT}

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	2026-05-18T03:46:15.463439Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b695a2a0a71d9e82cd8b9f50716c451cd23ebd4071c118cd22d202d03d60592f

Aliases

arxiv: 1001.1672 · arxiv_version: 1001.1672v2 · doi: 10.48550/arxiv.1001.1672 · pith_short_12: W2K2FIFHDWPI · pith_short_16: W2K2FIFHDWPIFTML · pith_short_8: W2K2FIFH

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/W2K2FIFHDWPIFTMLT5IHC3CFDT \
  | 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: b695a2a0a71d9e82cd8b9f50716c451cd23ebd4071c118cd22d202d03d60592f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "554d6ef55b6946def3c5fef7c0d4865a240d3a27983bca4c6e0b85e4fbb27644",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-01-11T15:08:41Z",
    "title_canon_sha256": "dfa75543bfa37d9befd245bc734fbe0e32f2c94ed16e4a8ea71986ff190c08ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.1672",
    "kind": "arxiv",
    "version": 2
  }
}