Pith Number

pith:FXMPMBLG

pith:2013:FXMPMBLGAHOPZIA2JXVILBU4PT

not attested not anchored not stored refs pending

The height of random $k$-trees and related branching processes

Alan Frieze, Colin Cooper, Ryuhei Uehara

arxiv:1309.4342 v3 · 2013-09-16 · math.CO · 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{FXMPMBLGAHOPZIA2JXVILBU4PT}

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	2026-05-18T02:42:14.907473Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2dd8f6056601dcfca01a4dea85869c7ccc459653910594c38e676c6a6538ef1b

Aliases

arxiv: 1309.4342 · arxiv_version: 1309.4342v3 · doi: 10.48550/arxiv.1309.4342 · pith_short_12: FXMPMBLGAHOP · pith_short_16: FXMPMBLGAHOPZIA2 · pith_short_8: FXMPMBLG

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/FXMPMBLGAHOPZIA2JXVILBU4PT \
  | 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: 2dd8f6056601dcfca01a4dea85869c7ccc459653910594c38e676c6a6538ef1b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4c8e2e1f8472551ccefdfa9019b09fe107dc48e619e13ab9fc28d95c14a24d2",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-09-16T16:58:22Z",
    "title_canon_sha256": "4d0159bc876f1b8e3384a35d53cfffe73a75a77b23af6b7a4ead2577117e51bb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.4342",
    "kind": "arxiv",
    "version": 3
  }
}