Pith Number

pith:OCDDK7JK

pith:2024:OCDDK7JKLSFUREB4AYAZE6IWKC

not attested not anchored not stored refs pending

The Critical Beta-splitting Random Tree III: The exchangeable partition representation and the fringe tree

David J. Aldous, Svante Janson

arxiv:2412.09655 v1 · 2024-12-12 · math.PR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OCDDK7JKLSFUREB4AYAZE6IWKC}

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	2026-07-05T09:48:39.662980Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7086357d2a5c8b48903c06019279165081436a714da113330634169d7131d53c

Aliases

arxiv: 2412.09655 · arxiv_version: 2412.09655v1 · doi: 10.48550/arxiv.2412.09655 · pith_short_12: OCDDK7JKLSFU · pith_short_16: OCDDK7JKLSFUREB4 · pith_short_8: OCDDK7JK

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/OCDDK7JKLSFUREB4AYAZE6IWKC \
  | 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: 7086357d2a5c8b48903c06019279165081436a714da113330634169d7131d53c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4a7566d1e71ebd3fa7fd04a899421516d2a4abbe92207127f096d79efa74a203",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2024-12-12T02:02:03Z",
    "title_canon_sha256": "7752decb51544bcc1bf3efe987c67e05cd807752e620bcfb4005e364c918c2b8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.09655",
    "kind": "arxiv",
    "version": 1
  }
}