Pith Number

pith:2MASO76T

pith:2024:2MASO76TXYQ4I4EAYKDULF3FIB

not attested not anchored not stored refs pending

The multiple birth properties of multi-type Markov branching processes

Junping Li, Wanting Zhang

arxiv:2407.05252 v1 · 2024-07-07 · 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{2MASO76TXYQ4I4EAYKDULF3FIB}

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	2026-07-05T08:41:10.150966Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d301277fd3be21c47080c2874597654047e923a8418db53d85b3f7742ef9929b

Aliases

arxiv: 2407.05252 · arxiv_version: 2407.05252v1 · doi: 10.48550/arxiv.2407.05252 · pith_short_12: 2MASO76TXYQ4 · pith_short_16: 2MASO76TXYQ4I4EA · pith_short_8: 2MASO76T

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/2MASO76TXYQ4I4EAYKDULF3FIB \
  | 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: d301277fd3be21c47080c2874597654047e923a8418db53d85b3f7742ef9929b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "120e8bfc3c231e9e0fa074eccab36663327fbbed1539fad0769b4b12a8ffb461",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2024-07-07T03:59:40Z",
    "title_canon_sha256": "0560dd9d5946edf5fa56dc09f44d6a5422b689931e80943a523bbf85260a0b8c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2407.05252",
    "kind": "arxiv",
    "version": 1
  }
}