Pith Number

pith:ZU7ASJKZ

pith:2013:ZU7ASJKZ6KB3CY54VPG3IECVJL

not attested not anchored not stored refs pending

On the expected time a branching process has K individuals alive

Peter Neal, Tom Britton

arxiv:1304.8014 v1 · 2013-04-30 · 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{ZU7ASJKZ6KB3CY54VPG3IECVJL}

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	2026-05-18T03:26:51.148744Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd3e092559f283b163bcabcdb410554af7d094c9009472f2da344b3c71e60677

Aliases

arxiv: 1304.8014 · arxiv_version: 1304.8014v1 · doi: 10.48550/arxiv.1304.8014 · pith_short_12: ZU7ASJKZ6KB3 · pith_short_16: ZU7ASJKZ6KB3CY54 · pith_short_8: ZU7ASJKZ

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/ZU7ASJKZ6KB3CY54VPG3IECVJL \
  | 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: cd3e092559f283b163bcabcdb410554af7d094c9009472f2da344b3c71e60677

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c98c4b7ec6f6e6aad1fddfae58c1fb1ec822d42c020ff080d345f353f4c7d858",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-04-30T14:41:26Z",
    "title_canon_sha256": "9172ac3614be31a78c344d59cf0ca49c052b2f15fdddc9de87129a0205a31914"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.8014",
    "kind": "arxiv",
    "version": 1
  }
}