Pith Number

pith:MU2DFPQX

pith:2023:MU2DFPQXYTTIDF6NHJCZQKEOVR

not attested not anchored not stored refs pending

The Critical Beta-splitting Random Tree: Heights and Related Results

Boris Pittel, David Aldous

arxiv:2302.05066 v4 · 2023-02-10 · math.PR

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\usepackage{pith}
\pithnumber{MU2DFPQXYTTIDF6NHJCZQKEOVR}

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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

The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height

Receipt and verification

First computed	2026-07-05T09:03:46.745371Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

653432be17c4e68197cd3a4598288eac40bb92a2cd6147ee0bcb4b1c3e8ac95a

Aliases

arxiv: 2302.05066 · arxiv_version: 2302.05066v4 · doi: 10.48550/arxiv.2302.05066 · pith_short_12: MU2DFPQXYTTI · pith_short_16: MU2DFPQXYTTIDF6N · pith_short_8: MU2DFPQX

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/MU2DFPQXYTTIDF6NHJCZQKEOVR \
  | 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: 653432be17c4e68197cd3a4598288eac40bb92a2cd6147ee0bcb4b1c3e8ac95a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "69bf6cf36d2af9a69fdb9aeff6daf1e76d81179f9d450ad3c0ab1a9b3dd2a2d9",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2023-02-10T05:55:13Z",
    "title_canon_sha256": "2fc9c5425f70b39dc477842ef09fa220b7a686a5be7427bfd3e5e5175baba7d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2302.05066",
    "kind": "arxiv",
    "version": 4
  }
}