Pith Number

pith:PNCH52OQ

pith:2014:PNCH52OQ2AHSFSDSMHKN4NNHC4

not attested not anchored not stored refs pending

Asymptotic behavior of critical irreducible multi-type continuous state and continuous time branching processes with immigration

Gyula Pap, Matyas Barczy

arxiv:1404.2242 v3 · 2014-04-08 · 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{PNCH52OQ2AHSFSDSMHKN4NNHC4}

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	2026-05-18T01:10:41.461483Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b447ee9d0d00f22c87261d4de35a71737cec2ed70388263eddab090d7cf9835

Aliases

arxiv: 1404.2242 · arxiv_version: 1404.2242v3 · doi: 10.48550/arxiv.1404.2242 · pith_short_12: PNCH52OQ2AHS · pith_short_16: PNCH52OQ2AHSFSDS · pith_short_8: PNCH52OQ

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/PNCH52OQ2AHSFSDSMHKN4NNHC4 \
  | 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: 7b447ee9d0d00f22c87261d4de35a71737cec2ed70388263eddab090d7cf9835

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff981af17c4fdec1f633eead3643cacb9978f0810183d6568735f6008e43b708",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-04-08T18:29:26Z",
    "title_canon_sha256": "3304e1c5b1dec4f0ec41999d7486261bc875e8ea889b3a750a4b69a474386b5e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1404.2242",
    "kind": "arxiv",
    "version": 3
  }
}