Pith Number

pith:GO5U57G4

pith:2020:GO5U57G46NEYAZXPPDUDQ4TX56

not attested not anchored not stored refs pending

The down/up crossing properties of weighted Markov branching processes

Junping Li, Yanyun Li

arxiv:2001.02353 v4 · 2020-01-08 · 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{GO5U57G46NEYAZXPPDUDQ4TX56}

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	2026-07-05T00:55:46.880054Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

33bb4efcdcf3498066ef78e8387277efb3fb2f6654d1810f66d608546a9d3034

Aliases

arxiv: 2001.02353 · arxiv_version: 2001.02353v4 · doi: 10.48550/arxiv.2001.02353 · pith_short_12: GO5U57G46NEY · pith_short_16: GO5U57G46NEYAZXP · pith_short_8: GO5U57G4

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/GO5U57G46NEYAZXPPDUDQ4TX56 \
  | 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: 33bb4efcdcf3498066ef78e8387277efb3fb2f6654d1810f66d608546a9d3034

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "55098e930de4ab749658e0a838e3246b34226b393ee5480633e1df192c7bfe00",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2020-01-08T03:29:13Z",
    "title_canon_sha256": "0a5ea2e5ee36848bfbf8bdab2998a77f731154ac81397cdebd400a46a907c50b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2001.02353",
    "kind": "arxiv",
    "version": 4
  }
}