Pith Number

pith:57XZDIBE

pith:2017:57XZDIBEOAPY56JEEIW7VRZR6O

not attested not anchored not stored refs pending

Continuous-state branching processes with competition: duality and reflection at Infinity

Cl\'ement Foucart

arxiv:1711.06827 v3 · 2017-11-18 · 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{57XZDIBEOAPY56JEEIW7VRZR6O}

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	2026-05-18T00:04:45.205237Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

efef91a024701f8ef924222dfac731f3a554d4ba355e987efcbf3922a78591b8

Aliases

arxiv: 1711.06827 · arxiv_version: 1711.06827v3 · doi: 10.48550/arxiv.1711.06827 · pith_short_12: 57XZDIBEOAPY · pith_short_16: 57XZDIBEOAPY56JE · pith_short_8: 57XZDIBE

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/57XZDIBEOAPY56JEEIW7VRZR6O \
  | 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: efef91a024701f8ef924222dfac731f3a554d4ba355e987efcbf3922a78591b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e52911f7ef6f02bca2cfbe812d1bc392760beb20968d0a5350ac406ffc837caa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-11-18T08:36:43Z",
    "title_canon_sha256": "25d1d17ae926c2e24879fda4260c8ede6af6897e53134d0ea4633deced2ae346"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.06827",
    "kind": "arxiv",
    "version": 3
  }
}