Pith Number

pith:NGUHUAO6

pith:2013:NGUHUAO6IC7GUXEPEULHHHI5CF

not attested not anchored not stored refs pending

Escape from the boundary in Markov population processes

A. D. Barbour, Fima Klebaner, Haya Kaspi, kais Hamza

arxiv:1312.5788 v3 · 2013-12-20 · 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{NGUHUAO6IC7GUXEPEULHHHI5CF}

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	2026-05-18T02:40:10.850540Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

69a87a01de40be6a5c8f2516739d1d117f6e43437733d7bbb248c07dcc8c9bba

Aliases

arxiv: 1312.5788 · arxiv_version: 1312.5788v3 · doi: 10.48550/arxiv.1312.5788 · pith_short_12: NGUHUAO6IC7G · pith_short_16: NGUHUAO6IC7GUXEP · pith_short_8: NGUHUAO6

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/NGUHUAO6IC7GUXEPEULHHHI5CF \
  | 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: 69a87a01de40be6a5c8f2516739d1d117f6e43437733d7bbb248c07dcc8c9bba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b5866ea760aac35f2a9c4c7804adf1963404b3bc687149e9034fb6e024806fc3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-12-20T01:08:44Z",
    "title_canon_sha256": "757d68c5d06900821573f984c62da938b367e4b5340bdba0101d74ab0fe990e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.5788",
    "kind": "arxiv",
    "version": 3
  }
}