Pith Number

pith:ORKRYOPM

pith:2014:ORKRYOPM7QKQKPFV2T3I6VNZUQ

not attested not anchored not stored refs pending

Lyapunov exponents for branching processes in a random environment: The effect of information

Guy Latouche, Sophie Hautphenne

arxiv:1411.7531 v1 · 2014-11-27 · 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{ORKRYOPM7QKQKPFV2T3I6VNZUQ}

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	2026-05-18T02:32:37.751853Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

74551c39ecfc15053cb5d4f68f55b9a4189556bb089f36b524e616103d16d132

Aliases

arxiv: 1411.7531 · arxiv_version: 1411.7531v1 · doi: 10.48550/arxiv.1411.7531 · pith_short_12: ORKRYOPM7QKQ · pith_short_16: ORKRYOPM7QKQKPFV · pith_short_8: ORKRYOPM

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/ORKRYOPM7QKQKPFV2T3I6VNZUQ \
  | 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: 74551c39ecfc15053cb5d4f68f55b9a4189556bb089f36b524e616103d16d132

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42ebd2e8e40110931a066f961a53976bd9654790f079a34ee79a294f77571094",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-11-27T10:22:46Z",
    "title_canon_sha256": "0ea56b8d228aecb965698ab474589443b4c861f70962d3f25689df54305b078c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.7531",
    "kind": "arxiv",
    "version": 1
  }
}