Pith Number

pith:3S7WAE4R

pith:2011:3S7WAE4R3B5NQTCT7G2UXDTHMJ

not attested not anchored not stored refs pending

Catalytic branching processes via spine techniques and renewal theory

Leif Doering, Matthew I. Roberts

arxiv:1106.5428 v4 · 2011-06-27 · 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{3S7WAE4R3B5NQTCT7G2UXDTHMJ}

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	2026-05-18T04:00:52.260872Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dcbf601391d87ad84c53f9b54b8e676245bbcc50ad9a89ab25ddfd1920d5c174

Aliases

arxiv: 1106.5428 · arxiv_version: 1106.5428v4 · doi: 10.48550/arxiv.1106.5428 · pith_short_12: 3S7WAE4R3B5N · pith_short_16: 3S7WAE4R3B5NQTCT · pith_short_8: 3S7WAE4R

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/3S7WAE4R3B5NQTCT7G2UXDTHMJ \
  | 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: dcbf601391d87ad84c53f9b54b8e676245bbcc50ad9a89ab25ddfd1920d5c174

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c90d7e8a1efb6785e0d62ec4c7c057bde300b1cf62a0bcab04a38b1a77f2370",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-06-27T16:06:56Z",
    "title_canon_sha256": "374beb0e8816467fcfa33d46b98c50e28812bc3ce00e5fefdb5a8f6fce061621"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.5428",
    "kind": "arxiv",
    "version": 4
  }
}