Pith Number

pith:PWADSOKD

pith:2013:PWADSOKD3OU6SXX3QG2Y2Z5NOR

not attested not anchored not stored refs pending

Limit theorems for strongly and intermediately supercritical branching processes in random environment with linear fractional offspring distributions

Christian B\"oinghoff

arxiv:1311.1327 v2 · 2013-11-06 · 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{PWADSOKD3OU6SXX3QG2Y2Z5NOR}

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	2026-05-18T02:51:42.014373Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7d80393943dba9e95efb81b58d67ad7442dc55c6b9e62c3e0da5cca52942b89b

Aliases

arxiv: 1311.1327 · arxiv_version: 1311.1327v2 · doi: 10.48550/arxiv.1311.1327 · pith_short_12: PWADSOKD3OU6 · pith_short_16: PWADSOKD3OU6SXX3 · pith_short_8: PWADSOKD

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/PWADSOKD3OU6SXX3QG2Y2Z5NOR \
  | 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: 7d80393943dba9e95efb81b58d67ad7442dc55c6b9e62c3e0da5cca52942b89b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2beef033a64f7362e3715c852b69b45266225814377e512e7f01ba654e322f57",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-11-06T09:50:53Z",
    "title_canon_sha256": "470a73761436203594536d67e3a9f3c3bcf07d63fd3acf53a7178f61d244f464"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.1327",
    "kind": "arxiv",
    "version": 2
  }
}