Pith Number

pith:QZU6ARO7

pith:2020:QZU6ARO7JUDAHENROHZRJZ3K65

not attested not anchored not stored refs pending

The jumping properties of Markov branching processes

Junping Li, Yanyun Li

arxiv:2004.09261 v2 · 2020-04-17 · 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{QZU6ARO7JUDAHENROHZRJZ3K65}

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	2026-07-05T05:11:16.803329Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8669e045df4d060391b171f314e76af75314ea7221d567b6543693d4b26ef9ac

Aliases

arxiv: 2004.09261 · arxiv_version: 2004.09261v2 · doi: 10.48550/arxiv.2004.09261 · pith_short_12: QZU6ARO7JUDA · pith_short_16: QZU6ARO7JUDAHENR · pith_short_8: QZU6ARO7

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/QZU6ARO7JUDAHENROHZRJZ3K65 \
  | 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: 8669e045df4d060391b171f314e76af75314ea7221d567b6543693d4b26ef9ac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "37eab3bbe29c2bed85c0f0932610e6ca9936be729eed9c9dfb26e57473ccece6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2020-04-17T08:42:51Z",
    "title_canon_sha256": "f15196d9cd9281af481cba9e2662b1c6381357945502fb4348faebea26c62ad2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2004.09261",
    "kind": "arxiv",
    "version": 2
  }
}