Pith Number

pith:IRCMWPAQ

pith:2012:IRCMWPAQYZQQR5GIVUP2MIRVXR

not attested not anchored not stored refs pending

Heavy tailed branching process with immigration

Bojan Basrak, Rafa{\l} Kulik, Zbigniew Palmowski

arxiv:1207.6874 v1 · 2012-07-30 · 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{IRCMWPAQYZQQR5GIVUP2MIRVXR}

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	2026-05-18T03:49:48.372070Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4444cb3c10c66108f4c8ad1fa62235bc6d770e802f2301e5c3db0030042df482

Aliases

arxiv: 1207.6874 · arxiv_version: 1207.6874v1 · doi: 10.48550/arxiv.1207.6874 · pith_short_12: IRCMWPAQYZQQ · pith_short_16: IRCMWPAQYZQQR5GI · pith_short_8: IRCMWPAQ

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/IRCMWPAQYZQQR5GIVUP2MIRVXR \
  | 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: 4444cb3c10c66108f4c8ad1fa62235bc6d770e802f2301e5c3db0030042df482

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd72db7f03469d2fd7f679202b3c7a9ca8495918ec8740e86cc65b33e46ab420",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-07-30T09:32:04Z",
    "title_canon_sha256": "09829156fe993e9ea6749a14a67924675ad1f56fbe8b930d03fb4c129e65169d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.6874",
    "kind": "arxiv",
    "version": 1
  }
}