Pith Number

pith:3VXWG5KK

pith:2012:3VXWG5KKLRGE7MK3Y57NSQFGSI

not attested not anchored not stored refs pending

Asymptotic behavior of critical primitive multi-type branching processes with immigration

Gyula Pap, M\'arton Isp\'any

arxiv:1205.0388 v1 · 2012-05-02 · 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{3VXWG5KKLRGE7MK3Y57NSQFGSI}

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	2026-05-18T03:56:34.660559Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd6f63754a5c4c4fb15bc77ed940a6921966d85f1551488e75685fdc3b1bda81

Aliases

arxiv: 1205.0388 · arxiv_version: 1205.0388v1 · doi: 10.48550/arxiv.1205.0388 · pith_short_12: 3VXWG5KKLRGE · pith_short_16: 3VXWG5KKLRGE7MK3 · pith_short_8: 3VXWG5KK

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/3VXWG5KKLRGE7MK3Y57NSQFGSI \
  | 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: dd6f63754a5c4c4fb15bc77ed940a6921966d85f1551488e75685fdc3b1bda81

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "75f8685bb33393849b829c9db4c43fd8b8e88c5e8c409698a62f25c3db4fd969",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-05-02T11:41:49Z",
    "title_canon_sha256": "9a90813f8c96ec6eb8f84d1d4d278ecca4bc3d04e1865c4f3dfeefe1b0ae1377"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.0388",
    "kind": "arxiv",
    "version": 1
  }
}