Pith Number

pith:DIC2G72R

pith:2023:DIC2G72RKGJJY7ZJ2Q6VCDGZ62

not attested not anchored not stored refs pending

The Critical Beta-splitting Random Tree II: Overview and Open Problems

David J. Aldous, Svante Janson

arxiv:2303.02529 v3 · 2023-03-04 · math.PR · math.CO · q-bio.PE

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DIC2G72RKGJJY7ZJ2Q6VCDGZ62}

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.

Cited by

1 paper in Pith

Asymptotics for the harmonic descent chain and applications to critical beta-splitting trees

Receipt and verification

First computed	2026-07-05T10:50:40.147973Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1a05a37f5151929c7f29d43d510cd9f69cecff1caec9f003259f6b0a4e952b63

Aliases

arxiv: 2303.02529 · arxiv_version: 2303.02529v3 · doi: 10.48550/arxiv.2303.02529 · pith_short_12: DIC2G72RKGJJ · pith_short_16: DIC2G72RKGJJY7ZJ · pith_short_8: DIC2G72R

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/DIC2G72RKGJJY7ZJ2Q6VCDGZ62 \
  | 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: 1a05a37f5151929c7f29d43d510cd9f69cecff1caec9f003259f6b0a4e952b63

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87cd4b51a2748e33ec433619f0681546545db9351be2ffe88243fd47355c4918",
    "cross_cats_sorted": [
      "math.CO",
      "q-bio.PE"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2023-03-04T23:46:05Z",
    "title_canon_sha256": "1f39481860a04e1bae55dc162916ef035f5e2fcd8074d195bf5e658bfc67d104"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2303.02529",
    "kind": "arxiv",
    "version": 3
  }
}