Pith Number

pith:67LE5NED

pith:2012:67LE5NEDAG64QG6XMIUMPS7AUU

not attested not anchored not stored refs pending

Lower large deviations for supercritical branching processes in random environment

Christian Boeinghoff, Vincent Bansaye (CMAP)

arxiv:1210.4264 v3 · 2012-10-16 · 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{67LE5NEDAG64QG6XMIUMPS7AUU}

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	2026-05-18T00:53:21.406512Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7d64eb48301bdc81bd76228c7cbe0a536d73cf96e76b7b253965e3ea35501fe

Aliases

arxiv: 1210.4264 · arxiv_version: 1210.4264v3 · doi: 10.48550/arxiv.1210.4264 · pith_short_12: 67LE5NEDAG64 · pith_short_16: 67LE5NEDAG64QG6X · pith_short_8: 67LE5NED

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/67LE5NEDAG64QG6XMIUMPS7AUU \
  | 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: f7d64eb48301bdc81bd76228c7cbe0a536d73cf96e76b7b253965e3ea35501fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb81a8b87feb014e72ab2dfb3c9c7c8248185d0361ddb1164c00a891589b46c0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-10-16T06:36:32Z",
    "title_canon_sha256": "140af7ec8b2ad4dda74d9b65a9e781b19da1bff44f93781eb724799638ee2819"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.4264",
    "kind": "arxiv",
    "version": 3
  }
}