Pith Number

pith:NIGXEM24

pith:2009:NIGXEM24D4GZ6RDINYM7HBRNE5

not attested not anchored not stored refs pending

A law of large numbers approximation for Markov population processes with countably many types

A.D. Barbour, M.J. Luczak

arxiv:1001.0044 v3 · 2009-12-30 · 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{NIGXEM24D4GZ6RDINYM7HBRNE5}

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	2026-05-18T04:25:26.058085Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a0d72335c1f0d9f44686e19f3862d2766422a4e9b1c7eb9853ae24853476cf6

Aliases

arxiv: 1001.0044 · arxiv_version: 1001.0044v3 · doi: 10.48550/arxiv.1001.0044 · pith_short_12: NIGXEM24D4GZ · pith_short_16: NIGXEM24D4GZ6RDI · pith_short_8: NIGXEM24

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/NIGXEM24D4GZ6RDINYM7HBRNE5 \
  | 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: 6a0d72335c1f0d9f44686e19f3862d2766422a4e9b1c7eb9853ae24853476cf6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f839e502a04984c24b863808636f52c872f0c211d156350087c5d2646538d52f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-12-30T23:08:46Z",
    "title_canon_sha256": "6eae713d06769727794e925fa5b791bd109774996257857487efaf9faa6ece02"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.0044",
    "kind": "arxiv",
    "version": 3
  }
}