Pith Number

pith:UUBE6NPM

pith:2019:UUBE6NPMBOP4VZSGPJGZNXPA4Q

not attested not anchored not stored refs pending

Continuous-state branching processes with immigration

Zenghu Li

arxiv:1901.03521 v1 · 2019-01-11 · 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{UUBE6NPMBOP4VZSGPJGZNXPA4Q}

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	2026-05-17T23:56:31.027168Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a5024f35ec0b9fcae6467a4d96dde0e425195f16fc8e6adc68631e6061a23e60

Aliases

arxiv: 1901.03521 · arxiv_version: 1901.03521v1 · doi: 10.48550/arxiv.1901.03521 · pith_short_12: UUBE6NPMBOP4 · pith_short_16: UUBE6NPMBOP4VZSG · pith_short_8: UUBE6NPM

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/UUBE6NPMBOP4VZSGPJGZNXPA4Q \
  | 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: a5024f35ec0b9fcae6467a4d96dde0e425195f16fc8e6adc68631e6061a23e60

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "caea01eb7d03bf99bce7dca2f5e33912deb6b5c3d1ce77bbd82a60a2fcc7c2ed",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-01-11T09:21:11Z",
    "title_canon_sha256": "38646a373d99b6dac92356335411058f4666fdae93d7abe94e7439a2e46cba92"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1901.03521",
    "kind": "arxiv",
    "version": 1
  }
}