Pith Number

pith:J47AKOCI

pith:2026:J47AKOCIWHKX3PZAVI42TOLP5F

not attested not anchored not stored refs pending

Explosion and non-explosion in pure birth Crump--Mode--Jagers branching processes

Andrii Ilienko, Oleksii Galganov

arxiv:2601.06850 v2 · 2026-01-11 · 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{J47AKOCIWHKX3PZAVI42TOLP5F}

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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.

Cited by

1 paper in Pith

A counter-example to persistence in generalised preferential attachment trees

Receipt and verification

First computed	2026-06-12T01:08:20.920854Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f3e053848b1d57dbf20aa39a9b96fe95fda08ff8afca881a8916a80f4b6447c

Aliases

arxiv: 2601.06850 · arxiv_version: 2601.06850v2 · doi: 10.48550/arxiv.2601.06850 · pith_short_12: J47AKOCIWHKX · pith_short_16: J47AKOCIWHKX3PZA · pith_short_8: J47AKOCI

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/J47AKOCIWHKX3PZAVI42TOLP5F \
  | 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: 4f3e053848b1d57dbf20aa39a9b96fe95fda08ff8afca881a8916a80f4b6447c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9f78456be8822d609c33a0f6d0d020ab0f26174887a3eda0a531018053395496",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-01-11T10:45:25Z",
    "title_canon_sha256": "ce8996461a1941d1ef1665ee44c4f1b40b35f8b122263f4f2936ca0028101f7f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.06850",
    "kind": "arxiv",
    "version": 2
  }
}