Pith Number

pith:FC43AR3U

pith:2015:FC43AR3U4LEC42EMZBWXHT7R25

not attested not anchored not stored refs pending

n-type Markov Branching Processes with Immigration

Juan Wang, Junping Li, Yanchao Zang

arxiv:1512.04696 v1 · 2015-12-15 · 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{FC43AR3U4LEC42EMZBWXHT7R25}

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	2026-05-18T01:24:19.653042Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

28b9b04774e2c82e688cc86d73cff1d765cf2f007dbdf13e543783a4b7b0214a

Aliases

arxiv: 1512.04696 · arxiv_version: 1512.04696v1 · doi: 10.48550/arxiv.1512.04696 · pith_short_12: FC43AR3U4LEC · pith_short_16: FC43AR3U4LEC42EM · pith_short_8: FC43AR3U

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/FC43AR3U4LEC42EMZBWXHT7R25 \
  | 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: 28b9b04774e2c82e688cc86d73cff1d765cf2f007dbdf13e543783a4b7b0214a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "983fd971065f14202bd79078f067c39395c2b51b069ecb3000a6ebc27d3dcf94",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-12-15T09:47:50Z",
    "title_canon_sha256": "e90b086499554e2f167deeb23b5dfb1075310efcb2baa5aa65d3bb1514f29063"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.04696",
    "kind": "arxiv",
    "version": 1
  }
}